Question

Obtain the ratio of secondary voltage to primary voltage in terms of number of turns in the two coils.

Answer 1

A transformer works on the principle of mutual induction. It changes the voltage levels without changing the frequency.

The output voltage (V_s > V_p) is raised by a step-up transformer. This is achieved by the secondary coil having more turns than the primary coil (N_s > N_p).

According to Faraday’s law of induction, the emf induced in each turn is the same (assuming perfect flux linkage).

The induced emf in the primary coil is:

ε_p = `-N_p (d phi)/dt`

The induced emf in the secondary coil is:

ε_s = `-N_s (d phi)/dt`

For an ideal transformer, the terminal voltages V_p and V_s are approximately equal to the emfs. Dividing the two equations:

`V_s/V_p = N_s/N_p` = k

Where k is the transformation ratio. For a step-up transformer, k > 1.