Question

Two coils A and B are connected in series with an ac source of emf 220 V (rms) and frequency 50 Hz. The resistance of A is 4$\Omega$ and inductance of B is 0.02 H. The power loss in the circuit is 3 KW and power factor is 0.75. Then, the resistance of coil B is:

• A. $0.5\Omega$
• B. $5\Omega$
• C. $5.075\Omega$
• D. $50.7\Omega$

Answer 1

The correct option is C $5.075\Omega$

Power loss in the circuit is given by:

$P=\frac{{220}^2}{\left|Z_{eq}\right|}\times 0.75=3000$

$\left|Z_{eq}\right|=12.1$

From definition of power factor,

$\frac{R_A+R_B}{\left|Z_{eq}\right|}=0.75$
$R_A+R_B=9.075$
$R_B=5.075\Omega$