What is a transformer? Explain construction and working of a transformer. Derive the equation for a transformer.

Answer: A transformer is a device that converts an alternating voltage of one value into an alternating voltage of another value (higher or lower) of the same frequency, working on mutual induction. Transformer equation: \(\dfrac{e_s}{e_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}\).

Construction: [Diagram: a rectangular laminated soft-iron core; primary coil of \(N_p\) turns on one limb connected to the a.c. input; secondary coil of \(N_s\) turns on the other limb connected to the load (output).]

• Two coils, the primary (\(N_p\) turns) and the secondary (\(N_s\) turns), insulated from each other, are wound on a common soft-iron core.
• The core is laminated (thin insulated sheets) to reduce eddy-current losses, and made of soft iron to reduce hysteresis loss and to link almost all the flux of the primary with the secondary.
• The a.c. input is applied to the primary; the output is taken from the secondary.

Working: The alternating current in the primary produces an alternating magnetic flux in the core. This changing flux links the secondary coil and induces an alternating e.m.f. in it by mutual induction, of the same frequency. If \(N_s \gt N_p\) it is a step-up transformer; if \(N_s \lt N_p\) it is a step-down transformer.

Derivation: Let \(\phi\) be the flux through each turn (same for both coils, assuming no flux leakage).

E.m.f. induced in the primary: \(e_p = -N_p\dfrac{d\phi}{dt}\) … (1)

E.m.f. induced in the secondary: \(e_s = -N_s\dfrac{d\phi}{dt}\) … (2)

Dividing (2) by (1): \(\dfrac{e_s}{e_p} = \dfrac{N_s}{N_p} = K\) (turns ratio).

For an ideal transformer (no energy loss), input power = output power: \(e_pI_p = e_sI_s\), so \(\dfrac{e_s}{e_p} = \dfrac{I_p}{I_s}\).

Hence \(\dfrac{e_s}{e_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}\). A step-up transformer increases voltage but decreases current in the same ratio.