JAMB UTME - Physics - 2024

The energy in a moving car is an example of 

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The energy in a moving car is an example of kinetic energy.

To explain simply, **energy** is the ability to do **work** or cause **change**. There are different forms of energy, and **kinetic energy** is one of them. It is defined as the energy possessed by an object due to its motion.

When a car is moving, it possesses **kinetic energy** because its components are in **motion**. This motion energy allows the car to do tasks, such as transporting people or goods from one place to another. The faster the car moves, the greater its **kinetic energy**, and thus it can make a larger impact or do more work.

In contrast, energy forms like **mechanical energy** is a combination of both kinetic and potential energy; **electrical energy** is associated with electrical charge movement, while **potential energy** is related to the position or condition of an object (like a car parked on a hill). Therefore, the specific type of energy from a moving car is **kinetic energy**.

Photometer is used to measure

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A photometer is an instrument designed to measure the intensity of light. It is used to determine how much light is received over a particular area. Photometers are vital in various fields such as photography, astronomy, and laboratory science for ensuring that light levels are appropriate for specific applications.

The device operates by assessing the brightness or illumination coming from a light source and comparing it with a standard light. The measurement can be displayed in different units such as lumens or lux, depending on the context of the measurement.

While photometers are focused on the intensity of light, they do not measure kinetic energy of liberated electrons, the frequency of light, or the wavelength of light. These quantities are measured using other specialized instruments, such as spectrometers or frequency analyzers.

In a Hare's apparatus, the height of water and a liquid X are 0.3m and 0.5m respectively. The relative density of x is?

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For Hare's apparatus

Relative density = hwhl $\frac{h_w}{h_l}$

Given: height of liquid = 0.5cm, height of water = 0.3cm

Relative density = 0.30.5 $\frac{0.3}{0.5}$ = 0.6

The part of the inner ear that is responsible for hearing is

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The part of the inner ear that is responsible for hearing is the cochlea.

The inner ear is a complex structure, and each of its components serves different functions. Let me break it down further:

• Cochlea: This is a spiral-shaped, fluid-filled structure that resembles a snail shell. It is the main organ responsible for hearing. Sound waves enter the ear, travel through the ear canal, and cause the eardrum to vibrate. These vibrations are then transmitted to the cochlea through tiny bones in the middle ear. Inside the cochlea, these vibrations create waves in the fluid, stimulating tiny hair cells. The movement of these hair cells converts the sound waves into electrical signals, which are sent to the brain through the auditory nerve, allowing us to perceive sound.


• Sacculus and Utriculus: These structures primarily deal with balance rather than hearing. They are part of the vestibular system, which helps the body maintain its balance and spatial orientation.


• Ampullae: These are located in the semicircular canals of the inner ear and also play a role in balance. They contain sensory hair cells that detect rotational movement of the head.

Thus, the cochlea is the crucial component of the inner ear responsible for converting sound vibrations into nerve signals, making it central to the process of hearing.

The device for measuring the angle of dip is 

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The device used for measuring the angle of dip is the dip circle.

Let me explain this in simple terms:

The angle of dip, also known as the magnetic inclination, is the angle made by the Earth's magnetic field lines with the horizontal plane. It varies depending on where you are on the Earth's surface. In some places, magnetic field lines are nearly vertical, while in others they are more horizontal.

A dip circle is a specialized scientific instrument used to measure this angle. It usually consists of a magnetic needle that is free to rotate in the vertical plane.

When using a dip circle, you align it so that its plane is parallel to the direction of the Earth's magnetic field. Then, you read the angle at which the magnetic needle stabilizes. This is the angle of dip. The instrument's mechanism allows for accurate measurement of this angle by compensating for any external influences or inclinations.

What is the inductance reactance of a coil of 7H when connected to a 50Hz a.c circuit?

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To determine the inductive reactance of a coil, we use the formula:

Inductive Reactance (X_L) = 2πfL

Where:

• X_L is the inductive reactance, measured in ohms (Ω)
• π is a constant approximately equal to 3.14159
• f is the frequency of the AC source, measured in hertz (Hz)
• L is the inductance of the coil, measured in henrys (H)

Given:

• Inductance (L) = 7 H
• Frequency (f) = 50 Hz

Substituting the given values into the formula:

X_L = 2 × π × 50 × 7

Calculating this:

X_L = 2 × 3.14159 × 50 × 7

X_L ≈ 2 × 3.14159 × 350

X_L ≈ 2 × 1099.557

X_L ≈ 2199.114

Therefore, the inductive reactance of the coil is approximately 2200Ω.

In the diagram above, the galvanometer is converted to 

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To determine what the galvanometer is converted to in the described scenario, let’s first understand how a galvanometer can be transformed into different measuring devices:

1. Galvanometer to Voltmeter: To convert a galvanometer into a voltmeter, a high resistance (known as a multiplier) is connected in series with the galvanometer. This high resistance ensures that the voltmeter can measure a wide range of voltages without drawing significant current from the circuit.

2. Galvanometer to Ammeter: To convert a galvanometer into an ammeter, a low resistance (called a shunt) is connected in parallel with the galvanometer. This allows the majority of the current to pass through the shunt, enabling the ammeter to measure high currents without damaging the galvanometer.

Since the problem statement does not specify any additional details, a general observation is that a galvanometer is commonly converted into an ammeter using a shunt, especially in basic electrical circuits where current measurement is necessary. Therefore, from the options provided, **the galvanometer is most likely converted to an ammeter**.

**In summary**, if a low resistance is added in parallel with the galvanometer, it becomes an ammeter, while adding a high resistance in series would convert it into a voltmeter. Since the context commonly involves conversion for current measurement, the provided diagram likely represents a galvanometer converted into an ammeter.

In electrolysis, when same quantity of electricity is passed through different electrolytes, mass of substances deposited is proportional to 

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In electrolysis, when the same quantity of electricity is passed through different electrolytes, the mass of substances deposited is proportional to their chemical equivalent. The reason for this lies in Faraday's laws of electrolysis. Faraday's second law states that the amounts of different substances deposited or liberated by the same quantity of electricity are proportional to their chemical equivalents.

Chemical equivalent refers to a measure of a substance's ability to react or be deposited during electrolysis, and it is calculated as the molar mass divided by valency (n). This is why it is sometimes also referred to as equivalent weight.

In essence, for a given charge (equal number of electrons or electricity), a substance with a lower chemical equivalent will deposit more mass because it requires fewer electrons to undergo the chemical change.

Newton's law of cooling is valid only for a 

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Newton's Law of Cooling states that the rate of heat loss of an object is directly proportional to the difference in temperature between the object and its surroundings, provided that this temperature difference is small.

Therefore, this law is only valid within a small temperature range.

The value of R required to make the galvanometer measure voltage up to 40V in the diagram above 

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In a galvanometer setup intended to measure voltages, you often encounter a configuration known as a voltmeter, where a resistor is added in series with the galvanometer to increase its range of measurement.

The basic principle is that the total resistance of the voltmeter (comprising the galvanometer's resistance and the additional series resistor) allows it to handle a higher voltage by limiting the current that flows through the galvanometer. The maximum voltage (V) that can be measured by the galvanometer is determined by Ohm's Law: V = I * R,

Where:

• V is the maximum voltage (40V in this case),
• I is the full scale current rating of the galvanometer,
• R is the total resistance needed so that the galvanometer is not damaged.

Assuming the galvanometer has a known internal resistance (G) and a known full-scale current (I_fullscale), the resistance R required in series can be calculated via the formula:

R = (V / I_fullscale) - G

For this solution, you need either the values of G and I_fullscale or their product (G * I_fullscale). Without those exact specifications provided, it would be imprudent to give an exact numeric answer.

However, if this is a typical example and you have a typical galvanometer with a full-scale current of 50 μA and an internal resistance of 500 Ω, you can compute:

R = (40 / 50 x 10^-6) - 500 = 2000 - 500 = 1500 Ω

Therefore, you would need an additional R = 1990 Ω - 1500 Ω = 490 Ω, meaning the closest possible practical value from your choices is 1990 Ω (including the internal resistance).

If the specific parameters of the galvanometer differ, adjust the calculation accordingly, but the general process is as laid out here.

Two points on a velocity-time graph have coordinates (2s, 5m/s) and (4s, 15m/s). Calculate the mean acceleration

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The mean acceleration of an object is determined by the change in velocity over the change in time. This is given by the formula:

Mean Acceleration (a) = (Final Velocity - Initial Velocity) / (Final Time - Initial Time)

From the velocity-time graph, we have the following points:

Initial Point: (2s, 5m/s)

Final Point: (4s, 15m/s)

Here, the Initial Velocity is 5m/s, the Final Velocity is 15m/s, the Initial Time is 2s, and the Final Time is 4s.

Plug these values into the formula:

Mean Acceleration (a) = (15m/s - 5m/s) / (4s - 2s)

Simplifying this, we get:

Mean Acceleration (a) = 10m/s / 2s = 5m/s²

The mean acceleration is therefore 5.0 m/s².

If the S.V.P of water vapour was 13.5mmHg at 33ºC and 7.3mmHg at 7ºC. Find the percentage relative of the air on a day when average air temperature was 33ºC and dew point was 7ºC.

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To calculate the percentage relative humidity of the air, we use the relationship between the saturation vapour pressure (SVP) and the actual vapour pressure. The formula for relative humidity is:

Relative Humidity (%) = (Actual Vapour Pressure / Saturation Vapour Pressure) * 100

In this problem, the "dew point" refers to the temperature at which air becomes saturated with moisture and water begins to condense. At the dew point, the actual vapour pressure is equal to the saturation vapour pressure at that dew point temperature.

From the problem, we have:

• Saturation Vapour Pressure (SVP) at 33ºC = 13.5 mmHg
• Saturation Vapour Pressure (SVP) at 7ºC (which is the dew point) = 7.3 mmHg

The actual vapour pressure of the air is equal to the SVP at the dew point, which is 7.3 mmHg.

Now we calculate the percentage relative humidity using the formula:

Relative Humidity (%) = (7.3 mmHg / 13.5 mmHg) * 100

Carrying out the calculation:

Relative Humidity (%) = (7.3 / 13.5) * 100 = 0.5407 * 100 = 54.07%

Rounding to the nearest whole number, we get **54%**. Therefore, the percentage relative humidity of the air is 54%.

What is the least possible error encountered when taking measurement with a metre rule?

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A standard meter rule has markings that are usually every millimeter (1 mm). The least count, which is the smallest measurement that can be accurately read, is often 1 mm.
The least possible error is generally considered to be half of the smallest division, so it is ±0.05cm (or ±0.5mm).

Find the amount of current required to deposit 0.02kg of metal in a given electrolysis for 120 seconds. [electro chemical equivalent of the metal = 1.3 x 10−7 ${}^{-7}$kgC−1 ${}^{-1}$]

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To determine the amount of current required, we need to use Faraday's laws of electrolysis. The first law states that the mass of the substance deposited at an electrode is directly proportional to the quantity of electricity (or charge) that passes through the electrolyte.

Here, we have:

• The mass of the metal deposited, \( m \), is 0.02 kg.
• The electrochemical equivalent, \( z \), is 1.3 x 10^-7 kg/C.
• The time during which the current is applied, \( t \), is 120 seconds.

According to Faraday's first law of electrolysis, the mass (\( m \)) can be calculated by the formula:

m = z \times I \times t

Where:

• m is the mass of the substance deposited (in kilograms).
• z is the electrochemical equivalent (in kg/Coulomb).
• I is the current (in amperes).
• t is the time (in seconds).

Rearranging the formula to solve for current \( I \):

I = \(\frac{m}{z \times t}\)

Substituting the given values into the formula:

I = \(\frac{0.02 \, \text{kg}}{1.3 \times 10^{-7} \, \text{kg/C} \times 120 \, \text{s}}\)

Calculating the denominator:

I = \(\frac{0.02}{1.56 \times 10^{-5}}\)

Solving for \( I \):

I = 1282.05 \, \text{A}

Thus, the appropriate amount of current required to deposit 0.02 kg of metal in 120 seconds is approximately 1.3 x 10³ A.

The energy stored in the above capacitor is 

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The energy stored in the capacitor = 12 $\frac{1}{2}$q2C $\frac{q^2}{C}$

Where C = 2F, q = 3C

=  12 $\frac{1}{2}$322 $\frac{3^2}{2}$ = 94 $\frac{9}{4}$ = 2.25J

How much joules of heat are given out when a piece of iron, of mass 60g and specific heat capacity 460JKg−1 ${}^{-1}$K−1 ${}^{-1}$, cools from 75ºC to 35ºC

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To find out how much heat is given out when the piece of iron cools down, we can use the formula for heat transfer:

Q = mcΔT

Where:

• Q = heat energy released or absorbed (in Joules, J)
• m = mass of the substance (in kilograms, kg)
• c = specific heat capacity (in Joules per kilogram per degree Celsius, J/Kg·K)
• ΔT = change in temperature (in degrees Celsius, °C)

First, let's list the values given and convert the mass from grams to kilograms:

• mass (m) = 60g = 0.06kg
• specific heat capacity (c) = 460 J/Kg·K
• initial temperature = 75ºC
• final temperature = 35ºC

Now, calculate the change in temperature:

ΔT = final temperature - initial temperature = 35ºC - 75ºC = -40ºC

Note: Since we are calculating the heat given out as the iron cools, the temperature change will be negative, which will make Q positive, indicating heat is released.

Substitute these values into the heat transfer formula:

Q = mcΔT = (0.06 kg) x (460 J/Kg·K) x (-40ºC)

Q = 0.06 x 460 x -40

Q = -1104 Joules

Since the question asks for how much heat is given out, we consider the positive value of Q, which is 1104J. Therefore, 1104J of heat is given out when the piece of iron cools from 75ºC to 35ºC.

The mechanical advantage of the machine shown above 

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Mechanical advantage of a machine = LOADEFFORT $\frac{\text{<br>}}{}$

In this case of a wedge, we can consider the dimensions given:

Load distance (height of the machine): 15 cm
Effort distance (movement of the effort): 0.5 cm

M.A = 150.5 $\frac{\mathrm{<br>}}{}$ = 30.0

The unit of impedance is 

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The unit of impedance is Ohm, which is symbolized by the Greek letter Ω (Omega). In electrical circuits, impedance (Z) is a measure of opposition that a circuit offers to the passage of electric current when a voltage is applied. It is similar to resistance but extends to alternating currents (AC) and contains the effects of resistance as well as reactance (which accounts for capacitors and inductors).

Just like resistance, the unit of impedance is the ohm because they measure similar concepts; however, impedance also accounts for phase shifts between voltage and current, which are not considered in simple resistance. Ohm's Law is used in AC circuits as Z = V/I, where Z is impedance, V is voltage, and I is current. This relationship shows why the unit of impedance is the same as that of resistance.

Electrolysis can be investigated using 

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When investigating electrolysis, the most relevant instrument from the list provided is the Voltameter. This is because the voltameter is specifically designed to measure the amount of substance that is deposited or consumed at electrodes during the electrolysis of an electrolyte. It functions based on the chemical change associated with the electric current passing through the electrolyte.

Here is a simple explanation of how electrolysis works and why a voltameter is useful:

Electrolysis is the process of using electricity to cause a chemical reaction, which is usually a decomposition reaction. This involves passing an electric current through an electrolyte (a substance containing free ions). These ions migrate towards electrodes, resulting in chemical changes. The key aspect to measure during electrolysis is the amount of material (e.g., metal or gas) that is deposited at the electrodes.

The Voltameter helps in understanding electrolysis because:

• It can measure the amount of electrons passing through the circuit, which relates directly to the mass of substances transformed at the electrodes according to Faraday's laws of electrolysis. These laws state that the amount of chemical change is proportional to the quantity of electricity passed.
• By measuring the quantity of the substance deposited, one can gain insights into the efficiency of the electrolytic process and how different variables (such as voltage and current) affect the process.

Voltmeter, Ammeter, and Galvanometer are not used primarily for investigating electrolysis:

• A Voltmeter measures electrical potential difference between two points in an electric circuit, which is useful for understanding voltage but not directly for measuring chemical changes in electrolysis.
• An Ammeter measures the current flowing through a circuit and provides information about the electrical aspects of the process but not the chemical changes.
• A Galvanometer detects and measures small electric currents, and while sometimes used to detect current flow, it is not specifically designed for measuring outcomes of electrolysis.

The dimension of power is 

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The dimension of power in physics is expressed in terms of the base units of mass (M), length (L), and time (T). Power is the rate at which work is done or energy is transferred over time, and it has the unit of watt (W) which is equivalent to one joule per second.

To derive the dimension of power:

1. Work has the dimension of energy, which is force applied over a distance. The dimension of work (or energy) is M L² T^-2 because force has the dimension M L T^-2 and distance adds another L.

2. Since power is work done per unit time, you would divide the dimension of work by time (T).

Thus, the dimensional formula for power is:

M L² T^-3

The simple form of the lead acid accumulator often has a negative pole of 

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The simple form of the lead acid accumulator often has a negative pole of lead plate. In a lead-acid battery, the key components include two electrodes and an electrolyte. The **negative pole**, also known as the cathode during discharge, is typically made of **lead (Pb)**, which is in the form of a **lead plate**. When the battery is in use or discharging, this lead reacts with sulphuric acid (the electrolyte) to create lead sulfate.

To break it down further:

• **The positive pole** is usually composed of a lead dioxide (PbO₂) plate, which is sometimes referred to as lead peroxide.
• **The electrolyte** in the lead-acid battery is a diluted sulphuric acid solution, but this is not a solid pole or electrode.
• **The negative pole** is simply a solid **lead plate**, as noted earlier.

Thus, by analyzing the composition and reactions within a lead-acid battery, it is clear that the **negative pole** is made from a **lead plate**.

A hydrometer of mass y kg and volume 2y x 10−5 ${}^{-5}$m3 ${}^3$ floats in a fluid with 20% of its volume above the fluid, what is the density of the fluid?

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To find the density of the fluid, we need to apply the principle of floatation, which states that the weight of the fluid displaced by the submerged part of the object is equal to the weight of the object. Let's walk through the steps:

Step 1: Understand the volume submerged

The hydrometer has a total volume of 2y x 10^-5 m³. It floats with 20% of its volume above the fluid. Hence, 80% of its volume is submerged in the fluid.

Submerged Volume, V_sub = (0.80) x (2y x 10^-5 m³) = 1.6y x 10^-5 m³

Step 2: Apply the principle of floatation

The weight of the fluid displaced equals the weight of the hydrometer.

Weight of hydrometer = Mass x Gravity = y kg x g (where g is the acceleration due to gravity). For the purpose of calculations, g can be considered as 9.81 m/s².

Weight of displaced fluid = Density of fluid (ρ_fluid) x Submerged Volume x g

According to the principle of floatation:

y x g = ρ_fluid x 1.6y x 10^-5 m³ x g

g is common on both sides and can be canceled out:

y = ρ_fluid x 1.6y x 10^-5

Step 3: Solving for the density of the fluid

ρ_fluid = y / (1.6y x 10^-5)

The y on both numerator and denominator cancels out:

ρ_fluid = 1 / (1.6 x 10^-5)

ρ_fluid = 6.25 x 10⁴ kg/m³

Thus, the density of the fluid is 6.25 x 10⁴ kg/m³.

A light ray passing from air into water at an angle of 30º from the normal in air would 

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When light passes from one medium to another, such as from air to water, it bends or refracts. This phenomenon is described by Snell's Law, which states: n₁ * sin(θ₁) = n₂ * sin(θ₂), where:

• n₁ is the refractive index of the first medium (air),
• θ₁ is the angle of incidence (the angle made by the light ray with the normal in the first medium),
• n₂ is the refractive index of the second medium (water),
• θ₂ is the angle of refraction (the angle made by the light ray with the normal in the second medium).

The refractive index of air is approximately 1, and the refractive index of water is approximately 1.33. Given the angle of incidence in air is 30º:

Using Snell's Law:

1 * sin(30º) = 1.33 * sin(θ₂)

You will find:

sin(θ₂) = sin(30º) / 1.33

sin(θ₂) ≈ 0.5 / 1.33

sin(θ₂) ≈ 0.375

Now, solve for θ₂ by taking the inverse sine (arcsin):

θ₂ ≈ arcsin(0.375)

θ₂ ≈ 22.09º

Thus, when a light ray passes from air into water at an angle of 30º from the normal in air, it will make an angle less than 30º from the normal in water, approximately 22.09º. This is because the light ray bends toward the normal as it enters a denser medium (water).

The formation of cilia and flagella in living cells is carried out with the help of

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The formation of cilia and flagella in living cells is primarily carried out with the help of **centrioles**.

Here's a simple explanation:

Centrioles are cylindrical structures made up of microtubules. They are found in eukaryotic cells and play a critical role in cell division and the organization of the cell's cytoskeleton. However, their role extends beyond this to the formation of the basal bodies which seed the growth of cilia and flagella.

Cilia and flagella are microscopic, hair-like structures that protrude from the surface of certain eukaryotic cells. They are primarily involved in movement. Cilia often work like tiny oars, moving fluid across the cell's surface or propelling single-celled organisms. Flagella are typically longer and move in a whip-like fashion to propel cells, such as sperm cells.

Here's how centrioles contribute to the formation of these structures:

1. **Basal Body Formation**: Each cilium or flagellum grows out from a structure known as a basal body. The basal body is derived from the centrioles. During this process, a centriole migrates to the cell's surface and acts as a nucleation site for the growth of microtubules, which in turn form the structural core of cilia and flagella.

2. **Microtubule Organization**: The centrioles help organize microtubules in a "9+2" arrangement, which is characteristic of cilia and flagella. This refers to nine pairs of microtubules forming a ring around two central microtubules, giving these structures both stability and flexibility for movement.

Thus, centrioles are crucial as they provide the groundwork for the formation and proper functioning of cilia and flagella. They ensure that these structures are assembled correctly and are able to carry out their roles in cell movement and fluid transport.

An accumulator is 90% efficient. If it gives out 2700J of energy while discharging, how much energy does it take in?

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In order to find out how much energy the accumulator takes in, given that it is 90% efficient and gives out 2700J of energy, we can use the formula for efficiency:

Efficiency = (Useful Energy Output / Total Energy Input) × 100%

Given:

Efficiency = 90%

Useful Energy Output = 2700J

We need to calculate the Total Energy Input (how much energy the accumulator takes in). Rearranging the formula to solve for Total Energy Input, we get:

Total Energy Input = Useful Energy Output / Efficiency

Substitute the known values:

Total Energy Input = 2700J / 0.9

Calculate the input:

Total Energy Input = 3000J

Therefore, the accumulator takes in 3000J of energy.

Find the value of a capacitor with voltage 5V and 30C.

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To find the value of the capacitance, we need to use the formula for capacitance:

Capacitance (C) = Charge (Q) / Voltage (V)

In this problem, the charge (Q) is given as 30 Coulombs (C) and the voltage (V) is 5 Volts (V). We can plug these values into the formula:

C = 30 C / 5 V

Calculating the above expression gives:

C = 6 Farads (F)

Therefore, the value of the capacitor is 6 Farads.

A particular household utilizes three electrical appliances for six hours daily if the appliances are rated 80W, 100W, and 120W respectively. Calculate the electrical bills paid monthly if an average month is 31 days. [1kwh = #24.08k]

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To calculate the monthly electrical bill, we first need to determine the total energy consumption of the household in kilowatt-hours (kWh). Here are the steps:

1. Calculate the total power consumption of the appliances daily:

• The appliances' power ratings are 80W, 100W, and 120W.
• Total power consumption: 80W + 100W + 120W = 300W.

2. Convert the daily power consumption from Watts to kilowatts (kW):

• Since 1kW = 1000W, the daily power consumption in kW is 300W / 1000 = 0.3 kW.

3. Calculate the energy used daily in kWh:

• The appliances are used for 6 hours daily.
• Energy used daily: 0.3 kW * 6 hours = 1.8 kWh.

4. Calculate the monthly energy consumption:

• An average month is 31 days.
• Monthly energy consumption: 1.8 kWh/day * 31 days = 55.8 kWh.

5. Calculate the cost based on the rate:

• The cost of electricity is ₦24.08 per kWh.
• Monthly electricity cost: 55.8 kWh * ₦24.08 = ₦1343.664.

Therefore, the monthly electrical bill is approximately ₦1343.66k.

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In a series resonant circuit, the current flowing in the circuit is at its maximum. Let me explain why:

In a series resonant circuit, we have a resistor (R), inductor (L), and capacitor (C) connected in series with an AC source. At a particular frequency called the resonant frequency, these circuits exhibit some unique characteristics. This resonant frequency is determined by the values of the inductor and capacitor and is given by the formula:

f₀ = 1 / (2π√(LC))

At the resonant frequency:

• The inductive reactance (X_L) and capacitive reactance (X_C) become equal in magnitude but opposite in phase. Thus, they cancel each other out.
• This causes the impedance (Z) of the circuit to be at its lowest value, equal to the resistance (R) of the circuit alone.
• Since impedance is at its minimum, according to Ohm’s law (V = IZ), the current through the circuit is at its maximum value for a given applied voltage.

Thus, in a series resonant circuit, when it is operating at its resonant frequency, the current flowing is at its maximum.

The diaphragm in the camera is similar to what part of the eyes?

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The diaphragm in a camera is similar to the iris in the human eye.

Here's a simple explanation:

• Both the diaphragm in a camera and the iris in the eye control the amount of light that enters. The diaphragm adjusts the size of the aperture, which is the opening that allows light to hit the camera's sensor.
• Similarly, the iris adjusts the size of the pupil, which is the opening that allows light to enter the eye and reach the retina.
• The camera's diaphragm is responsible for creating different aperture sizes, just as the iris changes the size of the pupil in different lighting conditions.
• In bright light, both the diaphragm and the iris make their respective openings smaller to reduce the amount of light entering, protecting the camera's sensor and the eye's retina respectively.
• Conversely, in low light conditions, both open wider to allow more light in, enhancing clarity and visibility.

In summary, the iris acts like a natural diaphragm, regulating the light that passes through the eye, much like the diaphragm does in a camera.

Using the diagram above, the effective force pushing it forward at an angle 60º is 

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To determine the effective force pushing the object forward at an angle of 60º, we need to resolve the given force into its components. Specifically, we are interested in the horizontal component of the force, as this is the part that effectively pushes the object forward.

The general formula to calculate the horizontal component of a force (F_x) when the force is applied at an angle (θ) is:

F_x = F * cos(θ)

Where:

• F is the magnitude of the force applied.
• θ is the angle at which the force is applied, in this case, 60º.
• cos(θ) is the cosine of the angle.

Assuming the magnitude of the force applied (F) is 50N, then the effective forward force can be calculated as follows:

F_x = 50N * cos(60º)

Using the trigonometric value:

cos(60º) = 0.5

Therefore:

F_x = 50N * 0.5

F_x = 25N

Hence, the effective force pushing it forward at an angle of 60º is 25.00N. Therefore, the correct answer is 25.00N.

The food nutrient with the highest energy value is

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Fat is the food nutrient with the highest energy value, providing 9 calories per gram, while carbohydrates and proteins provide 4 calories per gram. 

Fat is the body's most concentrated source of energy, providing more than twice as much potential energy as carbohydrates or proteins.However, carbohydrates burn fastest in metabolism. Fats are a type of lipid. Lipids are a group of organic compounds that are insoluble in water but soluble in organic solvents. Fats are solid at room temperature, while oils are liquid at room temperature. 

Therefore, the correct answer is option C.

An ideal transformer has

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An ideal transformer is a hypothetical concept used in electrical engineering to simplify the analysis of real transformers. In an ideal transformer, several assumptions are made to avoid losses and inefficiencies. Here's what an ideal transformer has:

No flux leakage: In an ideal transformer, it is assumed that all the magnetic flux generated in the primary coil is perfectly linked with the secondary coil. This means there is no flux leakage. This assumption ensures maximum efficiency, as all the energy is transferred from the primary to the secondary coil without losses.

Let's briefly discuss the other concepts to understand why they don't pertain to an ideal transformer:

Maximum primary resistance: In an ideal transformer, the resistance of the windings is assumed to be zero. If the primary has maximum resistance, it would result in power loss due to the resistance, contradicting the idea of an ideal transformer.

Hysteresis: This refers to the energy loss that happens in the core material due to the cyclic magnetization and demagnetization processes. An ideal transformer assumes there is no hysteresis loss, meaning the core material does not absorb any energy during these cycles.

Eddy current: These are loops of electric current induced within conductors by a changing magnetic field, which can cause significant energy loss. In an ideal transformer, it is assumed that there are no eddy currents, hence no energy loss due to this effect.

In summary, an ideal transformer is characterized by having no flux leakage, and it assumes that there are no losses due to resistance, hysteresis, or eddy currents. This makes the ideal transformer a perfect, lossless device for the purposes of theoretical analysis.

Mouth part adapted for piercing and sucking is found in

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The mouthpart adapted for piercing and sucking is found in the mosquito. Mosquitoes have a specialized mouth structure called a proboscis. This proboscis is long and slender, allowing mosquitoes to puncture the skin of their hosts and suck blood. The proboscis is a complex structure that contains several needle-like parts that make the piercing and sucking process efficient and effective.

The efficiency of a cell with internal resistance of 2Ω $\mathrm{\Omega }$ supply current to a 6Ω $\mathrm{\Omega }$ resistor is 

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To determine the efficiency of a cell with an internal resistance of 2 Ω while supplying current to a 6 Ω resistor, we can use the concept of power dissipation. Efficiency in this context is the ratio of the power delivered to the external resistor to the total power supplied by the cell. It can be calculated using the formula:

Efficiency (%) = (Power across load resistor / Total power output by cell) × 100

Let's break it down step by step:

• Step 1: Total Resistance - The total resistance in the circuit is the sum of the internal resistance and the resistance of the external resistor:
• Total Resistance (R_total) = Internal Resistance (R_internal) + External Resistance (R_load)
• R_total = 2 Ω + 6 Ω = 8 Ω
• Step 2: Current Calculation - The current flowing through the circuit can be calculated using Ohm's Law, which states V = IR. Assume the electromotive force (EMF) of the cell is E volts:
• Current (I) = E / R_total
• I = E / 8 (Note: We keep E as a variable as it cancels out in the efficiency equation)
• Step 3: Power Delivered to Load - The power delivered to the external resistor can be calculated as:
• Power_load = I² × R_load
• Power_load = (E/8)² × 6
• Step 4: Total Power Supplied by the Cell - The total power supplied by the cell is given by:
• Power_total = EMF × Current = E × (E/8)
• Power_total = E² / 8
• Step 5: Calculate Efficiency: Finally, plug in the power values into the efficiency formula:
• Efficiency (%) = [(E/8)² × 6 / (E² / 8)] × 100
• Simplify to Efficiency (%) = [(6/8)] × 100 = 0.75 × 100 = 75%

The efficiency of the cell when supplying current to a 6 Ω resistor with an internal resistance of 2 Ω is 75%.

An effort of 40N is applied on a machine to lift a mass of 60kg. Determine the mechanical advantage of the machine [ g = 10ms2 ${}^2$ ]

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To determine the Mechanical Advantage (MA) of a machine, we use the formula:

MA = Load / Effort

Here, the Load is the weight of the mass being lifted, and the Effort is the force applied on the machine.

First, we need to calculate the Load. The Load is obtained by multiplying the mass of the object by the acceleration due to gravity (g = 10 m/s²).

So, the Load (weight of the mass) is:

Load = Mass × Gravity = 60 kg × 10 m/s² = 600 N

The Effort given is 40 N.

Now, we can calculate the Mechanical Advantage:

MA = Load / Effort = 600 N / 40 N = 15

Therefore, the Mechanical Advantage of the machine is 15.

Calculate the depth of a swimming pool if the apparent depth is 10cm. ( Refractive index of water = 1.33 )

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To calculate the real depth of a swimming pool given the apparent depth, we can use the concept of refraction of light. When light passes from one medium to a denser medium, it bends towards the normal. This bending effect causes objects submerged in water to appear closer to the surface than they actually are. The formula to relate these depths is given by:

Real Depth = Apparent Depth × Refractive Index

Given the problem:

• Apparent Depth = 10 cm
• Refractive Index of water = 1.33

Using the formula:

Real Depth = 10 cm × 1.33

Calculating the above:

• Real Depth = 13.3 cm

Therefore, the depth of the swimming pool is 13.3cm.

Rainbow is formed when sunlight undergoes 

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A rainbow is formed through a combination of three processes: reflection, refraction, and dispersion. Let's break down each process to understand how a rainbow forms:

1. Refraction: When sunlight enters a raindrop, it bends or changes direction. This bending of light is known as **refraction**. Different colors of sunlight bend by different amounts because they have different wavelengths.

2. Reflection: Once inside the raindrop, the light gets reflected off the inside surface of the drop. This reflection sends the light back out of the raindrop at different angles.

3. Dispersion: As the light exits the raindrop, it bends again (refraction). Because each color bends by a different amount, the sunlight is spread out into its component colors, creating a spectrum. This spreading into a spectrum is called **dispersion**.

All three processes contribute to the formation of a rainbow. The combination of **refraction, reflection, and dispersion** results in the beautiful arc of colors that we see in the sky.

Calculate the power of an object which moves through a distance of 500cm in 1s on a frictionless surface by a horizontal force of 50N

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To calculate the power of an object, we need to use the formula for power in terms of work done over time. The formula is:

Power (P) = Work Done (W) / Time (t)

First, let's find the work done on the object. Work done can be calculated using the formula:

Work Done (W) = Force (F) × Distance (d)

Given:

• Force (F) = 50 N
• Distance (d) = 500 cm = 5 m (Note: We need to convert the distance from centimeters to meters because the unit of force is in newtons, and 1 m = 100 cm)

Substituting the values into the formula for work done, we get:

Work Done (W) = 50 N × 5 m = 250 Joules

Next, we consider the time it took for the object to move this distance:

• Time (t) = 1 s

Now, substituting the work done and time into the power formula:

Power (P) = 250 Joules / 1 s = 250 Watts

Thus, the power of the object is 250 Watts.

Calculate the value of electric field intensity due to a charge of 4μC if the force due to the charge is 8N

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To calculate the electric field intensity due to a charge, we need to use the formula:

Electric Field Intensity (E) = Force (F) / Charge (q)

In this problem, we are given that the force (F) is 8 Newtons (N) and the charge (q) is 4 microcoulombs (μC). First, we need to convert the charge from microcoulombs to coulombs:

1 microcoulomb (μC) = 1 x 10^-6 coulombs (C)

Therefore, 4 μC = 4 x 10^-6 C.

Now we can use the formula to find the electric field intensity:

E = F / q

E = 8 N / (4 x 10^-6 C)

E = 8 / 4 x 10⁶

E = 2 x 10⁶

Thus, the value of the electric field intensity is 2 x 10⁶ N/C.

A refrigerator uses 150W. If it is kept on for 336 hours non-stop, what is the energy consumed in KWh?

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To calculate the energy consumption of an appliance, you can use the formula:

Energy (in KWh) = Power (in kW) × Time (in hours)

First, convert the power rating of the refrigerator from watts (W) to kilowatts (kW). Since 1 kW is equal to 1000 W, you can convert 150W to kilowatts by dividing by 1000:

150 W = 0.150 kW

Next, calculate the energy consumed over the period the refrigerator is kept on, which is 336 hours. Use the formula:

Energy = 0.150 kW × 336 hours

Now, perform the multiplication:

Energy = 50.40 kWh

Therefore, when the refrigerator is kept on for 336 hours non-stop, it consumes 50.40 kWh of energy. This is the correct choice.