Question

A single phase transformer has a maximum efficiency of 90% at full load and unity power factor. The efficiency (in %) at half load at the same power factor is

Answer 1

At maximum efficiency copper losses equal to iron losses by using efficiency formula u can find out iron losses and substitute that value ,to find efficiency at half load

Answer 2

A single phase transformer has a maximum efficiency of 90% at full load and unity power factor.

We have to find the efficiency (in %) at half load at the same power factor.

We know, efficiency of single phase transformer is given by,

$\eta=\frac{L.Fcos\phi_2}{L.Fcos\phi_2+P_i+P_c}$

here L.F is the load factor, cosΦ₂ is the power factor , P_i and P_c are powers used in iron and copper respectively.

At full load ,

here, P_i = P_c

$\implies L.F=\sqrt{\frac{P_i}{P_c}}=1$

also cosΦ₂ = 1 [ unity power factor ]

∴ η = 0.9 = (1)/(1 + 2P_i)

⇒0.9 + 1.8P_i = 1

⇒P_i = 0.1/1.8

⇒P_i = 0.0555 Watt

at half load,

load factor, L.F = 1/2

⇒η = (0.5 × 1)/[0.5 × 1 + 0.555 × (1/2)² + 0.555] × 100

= 87.8 %

Therefore the efficiency is 87.8 % at half load at the same power factor.