The maximum flux density in the core of a 200/2000 V, 50 Hz single-phase transformer is 1.2 wb/m² . If the EMF per turn is 10 V, determine the primary and secondary turns, respectively.

E.M.F. Equation of a Transformer:

Consider,

N1 = No. of turns in the primary
ϕ_M = Maximum flux in core in Wb
f = Frequency of AC input in Hz

The flux increases from its zero value to maximum value Pm in one-quarter of the cycle as shown.

Note: The rate of change of flux per turn means induced EMF in volts.

The average rate of change of flux (Ea) per turns is given as,

If flux p is the instantaneous value of flux varies sinusoidally, then RMS. value of induced EMF is obtained by multiplying the average value with the form factor.

The form factor of a sinusoidal wave is 1.11

RMS value of EMF (Er) = 1.11 × average value of EMF (Ea)

Er = 1.11 × 4 f ϕM

Er = 4.44 f ϕM

If primary winding has N1 number of turns then primary RMS induced voltage (E1) is given as,

E1 = 4.44 f ϕM N1

Calculation:

Given,

E₁/N₁ =E₂/N2 = 10

E₁ = 200 V

E₂ = 2000 V

∴ N₁ = 200/10 = 20

and, N₂ = 2000/10 = 200