JAMB UTME - Physics - 2024

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When capacitors are connected in series, the formula to find their combined capacitance \(C_{\text{total}}\) is given by:

\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]

where \(C_1\) and \(C_2\) are the capacitances of the individual capacitors. In this case, \(C_1 = 0.0003 \, \mu\text{F}\) and \(C_2 = 0.0006 \, \mu\text{F}\).

First, calculate the reciprocal of each capacitance:

\[ \frac{1}{C_1} = \frac{1}{0.0003} \]

\[ \frac{1}{C_2} = \frac{1}{0.0006} \]

Calculating each value:

\[ \frac{1}{0.0003} = \frac{10^6}{3} \] and \[ \frac{1}{0.0006} = \frac{10^6}{6} \]

Now, add these values together:

\[ \frac{1}{C_{\text{total}}} = \frac{10^6}{3} + \frac{10^6}{6} = \frac{10^6 \times 2}{6} + \frac{10^6 \times 1}{6} = \frac{10^6 \times 3}{6} = \frac{10^6}{2} \]

Finally, take the reciprocal of the resulting value to find \(C_{\text{total}}\):

\[ C_{\text{total}} = \frac{2}{10^6} = 0.0002 \, \mu\text{F} \]

So, the combined capacitance of the two capacitors in series is 0.0002 μF.

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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

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To solve this problem, we need to understand the relationship between tension and frequency in a sonometer wire. The frequency of a vibrating string, such as one in a sonometer, is directly proportional to the square root of the tension in the string. Mathematically, this relationship is expressed as:

f ∝ √T

Where f is the frequency and T is the tension. In the given problem, the original frequency is 50 Hz, and the tension is increased to four times its original value. Let's analyze how this change in tension affects the frequency:

- Original tension = T

- New tension = 4T

Substitute the new tension into the formula:

f_new = 50 Hz × √(4T/T)

Simplify the equation:

f_new = 50 Hz × √4

f_new = 50 Hz × 2

f_new = 100 Hz

Thus, when the tension is four times the original tension, the new frequency of the sonometer's fundamental note becomes 100 Hz.

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To determine the effort needed to lift a load using a machine, we first need to understand some key concepts: **Load**, **Effort**, **Velocity Ratio** (VR), and **Efficiency**.

1. **Load** is the force or weight that needs to be lifted by the machine. In this case, the load is 300N.

2. **Velocity Ratio (VR)** is the ratio of the distance moved by the effort to the distance moved by the load. Given here as 2.

3. **Efficiency** of a machine is expressed as a percentage and is the ratio of the useful work output to the input work done by the effort. Here, the efficiency is 60% or 0.60 as a decimal.

The formula to calculate the **Effort** is derived from the relationship between these factors:

\[ \text{Efficiency} = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \]

Where:

\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}} \]

From the above, we have:

\[ \text{MA} = \text{VR} \times \text{Efficiency} \]

Replacing with the given values:

\[ MA = 2 \times 0.60 = 1.2 \]

Now, calculate the **Effort** using the relation:

\[ \text{Effort} = \frac{\text{Load}}{\text{MA}} \]

\[ \text{Effort} = \frac{300N}{1.2} = 250N \]

Therefore, the **Effort** needed to lift the load is 250N.

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To determine the weight of a bowling ball on the moon, we need to understand the relationship between weight, gravity, and mass.

Weight is the force exerted by gravity on an object. On Earth, this force depends on the object's mass and the acceleration due to gravity, which is approximately 9.8 m/s². Weight can be calculated using the formula:

Weight = Mass x Gravity

On the moon, the acceleration due to gravity is only ¹/₆ of Earth’s gravity. This means the gravitational pull on the moon is much weaker compared to the Earth. If we take the Earth's gravity to be 9.8 m/s², the moon's gravity would be:

Moon's Gravity = (9.8 m/s²) x (1/6) ≈ 1.63 m/s²

Given that the weight of an object is directly proportional to the gravitational force, the weight of an object on the moon would be substantially less than its weight on Earth. Thus, the weight of the bowling ball on the moon would be:

Weight on Moon = (Mass) x (1.63 m/s²) = ¹/₆ of its weight on Earth

Therefore, the weight of a bowling ball on the moon is ¹/₆ of its weight on Earth.

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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.

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Infra-red thermometers work by detecting the radiation from the body and converting it to temperature. These thermometers are designed to measure the infrared radiation, also known as heat radiation, emitted by objects. All objects with a temperature above absolute zero emit infrared radiation. The thermometer's sensor captures this radiation and converts it into an electrical signal that can be read as a temperature measurement. This method allows for quick, non-contact temperature readings, which is why infrared thermometers are often used in medical settings, industrial applications, and more.

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A thermometer that relies on the **thermometric property** of **change in volume with temperature** is the **Liquid-in-glass thermometer**.

Here is why:

1. **Construction**: A liquid-in-glass thermometer consists of a **glass tube** that encloses a small reservoir filled with a **thermometric liquid**, typically mercury or colored alcohol.

2. **Principle of Operation**: As the **temperature** changes, the **volume of the liquid** inside the tube changes. When the temperature rises, the liquid **expands** and moves up the tube. Conversely, when the temperature decreases, the liquid **contracts** and moves down the tube.

3. **Scale Calibration**: The thermometer has graduations marked along the tube, allowing the user to read the temperature by observing the level of the liquid against these scale markings.

Therefore, the liquid-in-glass thermometer operates on the principle that the **volume of a liquid changes with temperature**, making it the correct answer.

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The phenomenon of land and sea breeze is primarily attributed to convection.

To understand this, let's first look at what land and sea breezes are:

Land Breeze: At night, the land cools down faster than the sea. The cooler, denser air from the land moves towards the sea, and this is known as a land breeze.

Sea Breeze: During the day, the land heats up more quickly than the sea. The warmer, lighter air over the land rises, and the cooler air from the sea moves in to take its place. This movement of air from the sea to the land is known as a sea breeze.

Both of these processes involve the movement of air due to differences in temperature and density, which is essentially the process of convection.

Convection is the transfer of heat through a fluid (like air or water) and is responsible for moving air masses and creating these breezes. The warm air, being less dense, rises, and the cooler, denser air moves in to replace it.

In contrast, conduction is the transfer of heat through a solid material, and radiation is the transfer of heat in the form of electromagnetic waves, neither of which primarily drive the processes of these breezes, making convection the key player.

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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.

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The main feature of trees in the savanna habitat is the possession of thick, corky bark. The savanna is characterized by a distinct wet and dry season. During the dry season, fires are common as dry grasses and leaves become highly flammable. To adapt to this environmental condition, many trees in the savanna have developed a thick, corky bark which helps protect them against these frequent fires. This bark acts as an insulator, shielding the vital inner tissues of the tree from the heat of the flames. Additionally, this adaptation helps the trees retain moisture, which is crucial during the arid months when water is scarce.

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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

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An insulator is a material that has a very large energy gap between its valence band and conduction band. To understand this, let's first consider the concept of energy bands: In materials, electrons exist in different energy levels. These levels form bands called the valence band and the conduction band. A material is classified based on the size of the energy gap between these bands.

• Insulator: The energy gap is very large, which means electrons in the valence band require a lot of energy to jump to the conduction band where they can freely move. Because of this large gap, insulators do not conduct electricity well.
• Conductor: The valence band and conduction band overlap or have a very small gap, so electrons can move freely without requiring significant additional energy. Conductors actively conduct electricity.
• Semiconductor: The energy gap is moderate, which means some energy is required for electrons to move from the valence band to the conduction band. Semiconductors can conduct electricity under certain conditions, like when energy (in the form of heat or light) is provided.
• Intrinsic semiconductor: This is a pure type of semiconductor with no added impurities. It behaves like a semiconductor, having a moderate energy gap.

Thus, insulators have a very large energy gap band, making them poor conductors of electricity.

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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%.

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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.

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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.

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The magnetic force on an electron in a magnetic field (F) = q v Bsinθ $\theta$

B = 10T, q =  3 x 107 ${}^7$m/, θ $\theta$ = 60º and q =  1.6 x 10−19 ${}^{-19}$C

F =  1.6 x 10−19 ${}^{-19}$ x 3 x 107 ${}^7$ x 10 x sin 60º ≊ $\approxeq$ 4.162 × 10−11 ${}^{-11}$N

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The concept of an inclined plane is all about simplifying the forces involved in moving or holding a load. The **velocity ratio (VR)** for an inclined plane is defined as the ratio of the distance moved by the effort to the distance moved by the load. This can also be expressed in terms of the lengths involved in the triangle made by the inclined plane.

For an inclined plane placed at an angle **θ** to the horizontal, the velocity ratio is given by the formula:

VR = 1/sin(θ)

Given that the inclined plane is at an angle of **60º**:

First, find the sine of 60º:

sin(60º) = √3/2 (approximately 0.866)

Now, substitute this value into the formula for VR:

VR = 1/sin(60º) ≈ 1/0.866 ≈ 1.155

The **velocity ratio** for an inclined plane at **60º** to the horizontal is **approximately 1.155**.

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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

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The property by which a material returns to its original shape after the removal of force is called Elasticity.

Let's break it down:

Elasticity: This is a property of a material that allows it to return to its original shape or size after the force that caused deformation is removed. Think of a rubber band—you can stretch it, but once you let it go, it snaps back to its initial shape.

Ductility: This property refers to a material's ability to be stretched into a wire. For example, materials like copper are ductile because they can be drawn into thin wires without breaking.

Malleability: This is a material's ability to withstand deformation under compressive stress. It is the property that allows metals to be hammered or rolled into thin sheets. Gold is a good example of a malleable metal.

Plasticity: This property describes the material's ability to undergo permanent deformation without breaking. When a plastic region is reached, the material will not return to its original shape after the removal of force.

Therefore, when we speak of a material returning to its original shape after the removal of force, we are specifically referring to Elasticity.

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When a body moves in a straight line from one point, such as point P, to another point, such as point Q, the motion is called Translational Motion. This kind of motion refers to an object moving along a path in which every part of the object takes the same path as a reference point. This means that if you follow any point on the body, it covers the same amount of distance in the same time frame as any other point.

Let's break down the other options:

• Rotational Motion: This occurs when an object spins around an internal axis. For example, the rotation of the Earth on its axis is a rotational motion.


• Simple Harmonic Motion: This is a type of periodic motion where the restoring force is directly proportional to the displacement. An example of this is a pendulum swinging back and forth.


• Circular Motion: This occurs when an object moves along a circular path. For instance, the motion of the planets around the sun is circular motion.

In conclusion, since the body is moving from point P to point Q along a straight line, it exhibits Translational Motion.

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To calculate the quantity of heat absorbed or released by a substance, we can use the formula:

Q = C × ΔT

where:

• Q is the quantity of heat.
• C is the thermal capacity of the substance.
• ΔT is the change in temperature.

Given:

• C = 400 J/°C
• Initial temperature = 60°C
• Final temperature = 80°C

First, calculate the change in temperature:

ΔT = Final temperature - Initial temperature = 80°C - 60°C = 20°C

Now, substitute the values into the formula to find the quantity of heat:

Q = 400 J/°C × 20°C

Calculate the answer:

Q = 8000 J

Since the options provided are in kilojoules (KJ), we need to convert joules (J) to kilojoules (1 KJ = 1000 J):

Q = 8000 J ÷ 1000 = 8 KJ

Therefore, the quantity of heat for the copper rod, given the specified conditions, is 8 KJ.

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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.

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To find the apparent weight of a man of mass 60 kg standing in a descending lift, we first need to understand the concept of apparent weight. Apparent weight is the force that the man feels as his weight due to the reaction of the lift floor on him. When the lift accelerates, the apparent weight changes from his actual weight.

In this case, the lift is descending with a constant velocity of 3 m/s². Since the acceleration is downward, it means the lift is accelerating negatively compared to an upward acceleration.

The formula to find the apparent weight (W_apparent) when in a lift is:

W_apparent = m(g - a)

Where:

• m is the mass of the man, which is 60 kg
• g is the acceleration due to gravity, approximately 9.8 m/s²
• a is the acceleration of the lift (3 m/s² downward)

Substituting these values into the formula, we get:

W_apparent = 60 (9.8 - 3)

Calculating further:

W_apparent = 60 × 6.8

W_apparent = 408 N

The closest option to 408 N in the answers provided is 420 N. Therefore, the correct answer is 420 N.

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To find the area expansivity of a metal when given its cubic expansivity, you should understand the relationship between linear, area, and cubic expansivity.

Cubic expansivity (\( \beta \)) is defined as the fractional change in volume per change in temperature, and is given by the formula:

\[ \Delta V = \beta V \Delta T \]

Area expansivity (\( \alpha_{A} \)) corresponds to the fractional change in area per change in temperature and can be derived from the linear expansivity (\( \alpha \)). The relationship between these expansivities is as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = 2 \times \text{Linear Expansivity (\( \alpha \))} \]

The cubic expansivity (\( \beta \)) is related to the linear expansivity by:

\[ \text{Cubic Expansivity (\( \beta \))} = 3 \times \text{Linear Expansivity (\( \alpha \))} \]

Thus, based on these relationships, we can express the area expansivity in terms of the cubic expansivity:

\(\text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times \text{Cubic Expansivity (\( \beta \))}

Given that the cubic expansivity \( \beta \) is \( 3.9 \times 10^{-6} \, \text{K}^{-1} \):

The area expansivity can be calculated as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times 3.9 \times 10^{-6} \, \text{K}^{-1} = 2.6 \times 10^{-6} \, \text{K}^{-1} \]

Therefore, the **correct answer** is **2.6 x 10^{-6} K^{-1}**.

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The zone labelled II is called the littoral zone.

To explain: The littoral zone is a part of a body of water that is close to the shore. It is typically characterized by abundant sunlight and nutrient availability, making it a highly productive area for aquatic plants and animals. This zone supports various forms of life such as algae, small fish, and invertebrates. The key feature of the littoral zone is its proximity to the shoreline, where sunlight can penetrate to the bottom, allowing for photosynthesis to occur.

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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**.

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The degree of precision of a vernier caliper is actually the **smallest value** that the vernier scale can measure, which can be considered as the resolution or least count of the instrument. The degree of precision for most standard vernier calipers is 0.01 cm (or 0.1 mm). This means that the caliper can measure dimensions down to a hundredth of a centimeter.

To understand why this is the case, consider the construction of a vernier caliper:

• The main scale is similar to a ruler, usually graduated in centimeters and millimeters.
• The vernier scale, which moves with the sliding jaws, is marked such that some small fraction of its divisions aligns with one division on the main scale.

This alignment allows more precise measurements than the main scale alone. If the vernier scale has 10 divisions which coincide over a length equal to 9 divisions on the main scale, then each division of the vernier scale represents an extra 0.01 cm. Therefore, it allows measuring smaller intervals between the main scale markings very precisely.

Thus, you won't find vernier calipers with a degree of precision of 0.005 cm, 0.1 cm, or 1.0 cm as options in standard practice for precise measurement tools.

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A medium texture soil with high organic matter is best described as loamy soil. Here's why:

Loamy soil is a type of soil that is characterized by a balanced mixture of sand, silt, and clay particles. Because of this blend, loamy soil is not too coarse like sandy soil, nor is it too compact and dense like clay soil, making it a medium texture.

Moreover, loamy soil is renowned for its high organic matter content. This means that it contains a significant amount of decomposed plant and animal residues, which enrich the soil and provide essential nutrients for plant growth. This high organic content enhances the soil's fertility and structure, enabling it to retain moisture yet drain well, making it ideal for farming and gardening.

In conclusion, due to its balanced texture and richness in organic matter, loamy soil is the best fit for a medium-textured soil with high organic matter.

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The velocity ratio of a machine is a concept used to explain how much the machine is expected to amplify the input motion. If the velocity ratio of a machine is 4, it means that the distance moved by the effort is 4 times greater than the distance moved by the load.

To understand this concept better, consider what a machine does: it allows you to apply a small effort over a longer distance to move a heavy load over a shorter distance. In this scenario, if the velocity ratio is 4, then for every 4 meters (or units of distance) you exert effort, the load will move 1 meter (or unit of distance).

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To solve the problem, let's first understand the concept of efficiency in this context. Efficiency refers to the ratio of the useful power output to the total power output of a system. In simpler terms, it tells us how much of the power provided by the cell is being effectively used by the resistor, X.

Given that the cell has an internal resistance (r) of 2Ω and we need the efficiency to be 75%, we will follow these steps:

• The total resistance in the circuit is the sum of the internal resistance and the resistance of the resistor X, so it is (r + X).
• Efficiency is given by the formula:

Efficiency (%) = (R / (R + r)) * 100

Where:

• R is the resistance of resistor X.
• r is the internal resistance of the cell.

According to the problem, efficiency is 75%, so:

(X / (X + 2)) * 100 = 75

First, let’s eliminate the percentage by dividing both sides by 100:

(X / (X + 2)) = 0.75

Now, let's solve for X:

1. Multiply both sides by (X + 2):

X = 0.75 * (X + 2)



2. Distribute the 0.75:

X = 0.75X + 1.5



3. Subtract 0.75X from both sides:

0.25X = 1.5



4. Finally, divide by 0.25:

X = 1.5 / 0.25



5. Solve for X:

X = 6 Ω

Hence, for the cell to have an efficiency of 75%, the value of the resistor X must be 6Ω.

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A non-rechargeable cell, commonly known as a primary cell, is a type of chemical battery that is designed to be used once until the chemical reactions that produce electricity are exhausted. After this point, the cell cannot be reversed or recharged.

In the given examples, the dry leclanche cell is a well-known example of a non-rechargeable cell. It is commonly used in everyday devices like remote controls, wall clocks, and torches. This cell type utilizes zinc and manganese dioxide as electrodes and relies on a moist paste of ammonium chloride for the electrolyte.

The other examples, such as nickel iron, mercury cadmium, and lead-acid, involve rechargeable cells (secondary cells) that are specifically designed to endure multiple charges and discharges throughout their useful life. Thus, unlike the dry leclanche cell, these can be recharged after use.

Therefore, the dry leclanche cell is an ideal example of a non-rechargeable cell because it can only be used once. After depletion, it cannot be recharged or reused.

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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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To determine the energy of light given its frequency, we can utilize the formula:

E = h × f

Where:

E is the energy of the photon in joules (J)

h is Planck's constant, approximately 6.63 × 10^-34 J·s

f is the frequency of light in hertz (Hz)

Given the frequency f = 2.0 × 10¹⁵ Hz, we can substitute the known values into our equation:

E = 6.63 × 10^-34 J·s × 2.0 × 10¹⁵ Hz

To simplify the calculation, multiply the numerical parts and then add the indices of 10:

E = (6.63 × 2.0) × (10^-34 × 10¹⁵)

E = 13.26 × 10^-19 J

This can be approximated to 1.33 × 10^-18 J. Thus, the energy of light with the given frequency is 1.33 × 10^-18 J.

Antwortdetails

Hot wire ammeters measure current by detecting the heat produced in a wire due to the electric current flowing through it.

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The tangential force acting on an object that opposes it from sliding freely on the adjacent surface is called the friction force.

Let me explain each of the options to clarify why friction force is the correct answer:

• Normal force: This is the force exerted by a surface perpendicular (at a right angle) to the object resting on it. It supports the weight of the object, stopping it from passing through the surface. It is not tangential and does not oppose sliding; rather, it acts perpendicular to the surface.
• Friction force: This is the force that acts parallel to the surface contact between two objects or surfaces. It arises when one object tries to move over another. The friction force acts to oppose that movement, providing the necessary resistance to prevent sliding.
• Weight: This is the gravitational force acting downwards due to the mass of an object. It does not act tangentially on the surface but directly downwards towards the center of the Earth.
• Upthrust: Also known as buoyant force, this is the upwards force experienced by an object when it is immersed in a fluid (liquid or gas). It is responsible for the object floating or being pushed up, and is not related to tangential force or friction.

In summary, friction force is the force that acts to oppose sliding between surfaces in contact and acts tangentially, making it the correct answer.

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According to Faraday's laws of electromagnetic induction, an electromotive force (e.m.f) is induced in a conductor whenever it **cuts magnetic flux**. This means that for an e.m.f to be induced, the conductor must move in such a way that it intersects the magnetic lines of force. It is the relative motion between the conductor and the magnetic field that leads to the change in magnetic flux, resulting in the induction of e.m.f.

Let's explore why this is the correct answer using reasoning:

• When the conductor lies parallel to the magnetic flux: In this case, there is no motion or cutting of magnetic lines of force, leading to no change in magnetic flux through the conductor, and thus no e.m.f is induced.


• When the conductor lies in a magnetic field: Simply being within a magnetic field without any motion or change to the field does not induce e.m.f. There must be a change in the flux linkage for induction to occur.


• When the conductor lies outside but close to a magnetic field: Proximity alone without interaction doesn't change the magnetic flux linked with the conductor, thereby not inducing any e.m.f.


• When the conductor cuts magnetic flux: This is the condition necessary for the induction of e.m.f. The number of magnetic field lines interacting with the conductor changes, leading to a change in flux linkage, and consequently, e.m.f is induced.

Therefore, the phenomenon where a conductor cuts magnetic flux is essential for electromagnetic induction as per Faraday's laws.

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The device that operates based on the magnetic effect of electric current is the Dynamo.

To explain further, let's look at the concept of the magnetic effect of electric current:

• Magnetic Effect of Electric Current: When an electric current flows through a wire, it creates a magnetic field around the wire. This is known as the magnetic effect of electric current, and it is the fundamental principle behind devices and systems like electromagnets, electric motors, and dynamos.

A Dynamo is a device that converts mechanical energy into electrical energy. It operates based on the phenomenon called electromagnetic induction, which occurs due to the magnetic effect of electric current. When a coil of wire within the dynamo rotates in the presence of a magnetic field, it induces an electric current in the coil. Thus, the operation of a dynamo relies on the interaction between electric current and magnetic fields.

To contrast with other options:

• Electric Heater: It works on the principle of the heating effect of electric current, not the magnetic effect.
• Photocell: This device operates based on the photoelectric effect, which involves the conversion of light energy into electrical energy.
• Cold Cathode: This operates by the emission of electrons when a material is exposed to low-pressure gas discharge, and it doesn't rely on the magnetic effect of electric current.

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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.

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To calculate the distance between two objects based on the gravitational force acting between them, we need to use the formula for gravitational force:

F = (G * m1 * m2) / r²

Where:

• F is the gravitational force between the two masses (6.67 N).
• G is the gravitational constant (6.6 x 10^-11 Nm²/kg²).
• m1 is the first mass (10²⁴ kg).
• m2 is the second mass (10²⁷ kg).
• r is the distance between the centers of the two masses.

We need to compute r by rearranging the formula:

r² = (G * m1 * m2) / F

Therefore, the distance r is:

r = √((G * m1 * m2) / F)

Substitute the given values into the equation:

r = √((6.6 x 10^-11 Nm²/kg² * 10²⁴ kg * 10²⁷ kg) / 6.67 N)

Calculating inside the square root:

G * m1 * m2 = 6.6 x 10^-11 * 10²⁴ * 10²⁷ = 6.6 x 10⁴⁰ Nm²

Then divide by the force:

6.6 x 10⁴⁰ Nm² / 6.67 N = 0.99 x 10⁴⁰ m²

Finally, calculate the square root:

r = √(0.99 x 10⁴⁰)

r ≈ 1.0 x 10²⁰ m

Therefore, the distance between the two objects is approximately 1.0 x 10²⁰ m.