A 22 kVA, 2200/220 V, 50 Hz single-phase transformer has 1000 turns on its primary. Assuming it to be ideal, find (i) the transformation ratio, (ii) the number of secondary turns, (iii) the maximum flux in the core, (iv) the maximum flux density if t…

Answer: (i) \(K=0.1\); (ii) \(N_2=100\); (iii) \(\Phi_m=9.91\) mWb; (iv) \(B_m=0.991\) T; (v) \(I_1=10\) A, \(I_2=100\) A.

(i) \(K=\dfrac{V_2}{V_1}=\dfrac{220}{2200}=0.1\) (step-down).

(ii) \(N_2=KN_1=0.1\times1000=100\) turns.

(iii) From \(E_1=4.44\,f\,\Phi_mN_1\): \[\Phi_m=\frac{2200}{4.44\times50\times1000}=9.91\times10^{-3}\text{ Wb}=9.91\text{ mWb}.\]

(iv) \(B_m=\dfrac{\Phi_m}{A}=\dfrac{9.91\times10^{-3}}{100\times10^{-4}}=0.991\) T (Wb/m²).

(v) \(I_1=\dfrac{22000}{2200}=10\) A, \(I_2=\dfrac{22000}{220}=100\) A. Check: \(I_2/I_1=1/K=10\) ✓.