(a) Draw a simple labelled diagram illustrating the principle of a step-down transformer and explain how it works (b) State three ways by which energy is lo...

(a) Draw a simple labelled diagram illustrating the principle of a step-down transformer and explain how it works

 (b) State three ways by which energy is lost in a transformer and how they can be minimized.

(c) If a transformer is used to light a lamp rated at 60W, 220V from a 4400V a.c. supply, calculate the; (i) ratio of the number of turns of the primary coil to the secondary coil in the transformer (ii) current taken from the main circuit if the efficiency of the transforme is 95%.

Answer Details

a)

A step-down transformer: A step-down transformer is a device that decreases the voltage of an alternating current (AC) from the primary coil to the secondary coil. It consists of two coils of wire wrapped around a common iron core. The primary coil is connected to a source of high-voltage AC, while the secondary coil is connected to a load. The number of turns in the secondary coil is fewer than the number of turns in the primary coil.

The principle of a step-down transformer is based on electromagnetic induction. When an alternating current flows through the primary coil, it creates a changing magnetic field that induces a voltage in the secondary coil. The voltage induced in the secondary coil is proportional to the ratio of the number of turns in the primary coil to the number of turns in the secondary coil.

(b) Energy loss in a transformer: Energy is lost in a transformer due to several factors, including resistive losses, eddy current losses, and hysteresis losses. These losses can be minimized by using high-quality materials for the core and windings, by reducing the number of joints and connections, and by optimizing the design of the transformer.

(c)

1. Ratio of turns: The ratio of the number of turns of the primary coil to the secondary coil in a transformer can be calculated using the formula:
   N1/N2 = V1/V2
   Where N1 and N2 are the number of turns in the primary and secondary coils, respectively, and V1 and V2 are the voltages across the primary and secondary coils, respectively.
   In this case, V1 = 4400V, V2 = 220V, and N2/N1 = V2/V1 = 220/4400 = 1/20. Therefore, the ratio of the number of turns of the primary coil to the secondary coil is 20:1.
2. Current from the main circuit: The current taken from the main circuit can be calculated using the formula:
   P = VI
   Where P is the power in watts, V is the voltage in volts, and I is the current in amperes.
   In this case, P = 60W and V = 220V. The power delivered to the secondary coil is equal to the power supplied to the primary coil, minus the losses due to inefficiencies. Since the efficiency of the transformer is 95%, the power delivered to the primary coil is:
   P = P2/efficiency = 60W/0.95 = 63.16W
   Therefore, the current taken from the main circuit is:
   I = P/V = 63.16W/4400V = 0.0143A
   So, the current taken from the main circuit is 0.0143A.