Question

A household fan consumes 60 W and draws a current of 0.3125 A (rms) when connected to a 230 V (rms) ac, 50 Hz single-phase mains. The reactive power drawn by the fan in VAr is \(\underline{\hspace{2cm}}\) (rounded off to the nearest integer).

Hint:

The reactive power in an AC circuit can be calculated using \( Q = \sqrt{S^2 - P^2} \), where \( S \) is the apparent power and \( P \) is the real power.

Answer 1

Correct Answer: 39

The apparent power \( S \) is given by: \[ S = V_{\text{rms}} \times I_{\text{rms}} = 230 \times 0.3125 = 71.5 \, \text{VA} \] The real power \( P \) is given as 60 W. The reactive power \( Q \) can be calculated using the Pythagorean identity: \[ S^2 = P^2 + Q^2 \] Solving for \( Q \): \[ Q^2 = S^2 - P^2 = 71.5^2 - 60^2 = 5112.25 - 3600 = 1512.25 \] \[ Q = \sqrt{1512.25} \approx 38.9 \, \text{VAr} \] Rounding to the nearest integer: \[ Q \approx 39 \, \text{VAr} \] Thus, the reactive power drawn by the fan is \( 39 \, \text{VAr} \).