With the help of neat diagram explain construction of a transformer.Calculate energy required to build up current of 1A in an inductor of inductance 20 mH.

Answer: Energy required \(=0.01\) J

Construction of a transformer: [Figure: a rectangular laminated soft-iron core; the primary coil P (input AC) wound on one limb and the secondary coil S (output) on the other limb; the core links the flux of both coils.]

• A transformer has two coils of insulated copper wire, the primary (to which input AC is applied) and the secondary (from which output is taken), with \(N_P\) and \(N_S\) turns.
• The coils are wound on a common soft iron core, either on separate limbs or one over the other, so that almost all the magnetic flux produced by the primary links the secondary.
• The core is laminated (thin insulated sheets of soft iron, stalloy etc.) to reduce eddy-current losses; soft iron has low hysteresis loss and high permeability.
• The coils are insulated from each other and from the core. For a step-up transformer \(N_S\gt N_P\); for a step-down transformer \(N_S\lt N_P\). It works on mutual induction: \(\dfrac{e_S}{e_P}=\dfrac{N_S}{N_P}\).

Numerical: \(L=20\) mH \(=2\times10^{-2}\) H, \(I=1\) A.

Energy stored in the magnetic field of an inductor: \(E=\dfrac{1}{2}LI^2=\dfrac{1}{2}\times2\times10^{-2}\times1^2=10^{-2}\) J \(=0.01\) J.