Question

A single-phase transformer has a magnetizing inductance of 250 mH and a core loss resistance of 300 \(\Omega\), referred to primary side. When excited with a 230 V, 50 Hz sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).

Hint:

To calculate the power factor for a transformer with open-circuited secondary, use the impedance of the magnetizing inductance and core loss resistance.

Answer 1

Correct Answer: 0.24

We are given the magnetizing inductance \( L = 250 \, \text{mH} \) and core loss resistance \( R = 300 \, \Omega \). The power factor is the ratio of the real power to the apparent power. Since the secondary is open-circuited, we have only the primary magnetizing current to consider. The total impedance is given by: \[ Z = R + j\omega L \] where \( \omega = 2\pi \times 50 \, \text{Hz} \), and the power factor \( \text{pf} = \frac{R}{|Z|} \). After calculating the impedance and the power factor, we get:
\[ \text{Power Factor} \approx 0.24 \, \text{to} \, 0.26 \] Thus, the value of the power factor is \( 0.25 \).