Question

A given single-phase transformer supplies half the rated current to a load, at unity power factor, connected to its HV terminals at rated voltage. Calculate the magnitude of the supply voltage to be connected to its LV terminals.

Answer 1

The magnitude of the supply voltage to be connected to the LV terminals of a single-phase transformer is twice the magnitude of the primary voltage.

Step-by-step explanation:

To calculate the magnitude of the supply voltage to be connected to the LV terminals of a single-phase transformer, we need to use the transformer equation: the ratio of the secondary voltage to the primary voltage in a transformer equals the ratio of the number of turns in the secondary coil to the number of turns in the primary coil.

In this case, the load is at unity power factor, meaning the power factor is 1. Since the load is only drawing half the rated current, it means the current on the primary side is also half.

Let's say the primary voltage is V1, the primary current is I1, the secondary voltage is V2, and the secondary current is I2. According to the transformer equation, V2/V1 = N2/N1, where N2 is the number of turns in the secondary coil and N1 is the number of turns in the primary coil.

Since the load is drawing half the rated current, I2 = I1/2. Also, since the power factor is 1, the ratio of the primary current to the secondary current is equal to the ratio of the primary voltage to the secondary voltage: I1/I2 = V1/V2. Substituting the values we have, V1/(I1/2) = V1/V2. Solving for V2, we get V2 = 2V1.

Therefore, the magnitude of the supply voltage to be connected to the LV terminals is twice the magnitude of the primary voltage.