Question

With the help of a diagram, explain the principle of a device which changes a low ac voltage into a high voltage. Deduce the expression for the ratio of secondary voltage to the primary voltage in terms of the ratio of the number of turns of primary and secondary winding. For an ideal transformer, obtain the ratio of primary and secondary currents in terms of the ratio of the voltages in the secondary and primary coils.

Answer 1

                    Transformer

Use: It is a device that converts low ac voltage at high current into high ac voltage at low current and vice versa.

Principle: It consists of two coils P and S wound on a closed soft iron core. The coil that is fed from the ac supply is called the primary coil (P) and the other connected to the load is called the secondary coil (S). The core of the transformer is made of soft iron to reduce hysteresis loss and is laminated to reduce eddy current losses.

Working: When an alternating emf e_p is impressed on the primary winding, it sends an ac current through it, which sets up an alternating magnetic flux in the core. This induces an alternating emf e_s in the secondary. If N_P and N_s are the number of turns in the primary and secondary coils, their linkages with the flux are:

Φ_P = N_PBA  ...(B → Magnetic induction)

Φ_S = N_PBA  ...(A → Area of cross section)

The magnitude of the emf induced in the secondary

`e_S = (dphi_S)/(dt) = N_SA(dB)/(dt)`   ...(1)

The changing flux also induces an emf in the primary, whose magnitude

`e_P = (dphi_P)/(dt) = N_PA(dB)/(dt)`   ...(2)

From equations (1) and (2)

`("emf induced in secondary")/("voltage applied to primary") = (e_S)/(e_P) = N_S/N_P`   ...(3)

`N_S/N_P` = turns ratio or transformation ratio

If N_S > N_P, e_S > e_P → Such a transformer is called a step-up transformer.

If N_S < N_P, e_S < e_P → Such a transformer is called a step-down transformer.

In an ideal transformer

Instantaneous output power = instantaneous input power

e_Si_S = e_Pi_P   ...(4)

From equations (3) and (4)

`(e_S)/(e_P) = i_P/i_S = N_S/N_P`

In a step-up transformer, N_S > N_P, e_S > e_P but i_S < i_P

In a step-down transformer, N_S < N_P, e_S < e_P but i_S > i_P

At the generating station, a step-up transformer is used for stepping up the voltage and at the various receiving substations, a step-down transformer is used.