Question

A single -phase, 4 kVA, 200 V/100 V, 50 Hz transformer has laminated CRGO steel core shows rated no load loss of 500 W. When hv side winding is excited with 180 V, 45 Hz sinusoidal ac supply, the no load losses were measured 420 W. When hv side winding is excited by 100 V, 25 Hz sinusoidal ac source, the no load losses will be ________ W (upto 2 decimal place).

• A. 166.56

Answer 1

The correct option is A 166.56
$\text{For given single-phase transformer,}$

$\text{No load loss at 200 V, 50 Hz = 500 W}$

$\text{No load loss at 180 V, 45 Hz = 420 W}$

$\text{No load loss at 100 V, 25 Hz = x}$

$\text{Using condition of constant flux,}\varphi =V/F=constant$

$\frac{V}{f}=\frac{200}{50}=\frac{180}{45}=\frac{100}{25}$

$\text{So,}{P}_c=Af+B{f}^2$

$\text{For 50 Hz,}$ $500=A\left(50\right)+B(50{)}^2=50A+2500B$

$420=A\left(45\right)+B(45{)}^2=45A+2025B$

$\text{Solving simultaneously above equation,}$

$\text{A = 3.33, B = 0.1333}$

$\text{For frequency, f = 25 Hz}$

$P_c=3.33\times 25+0.1333\times 625$

$=83.25+83.313$

$\text{= 166.56 W}$