Question

The self-inductance of a choke coil is $10 \,mH$. When it is connected with a $10 \,V$ dc source, then the loss of power is $20$ watt. When it is connected with $10$ volt ac source loss of power is $10$ watt. The frequency of ac source will be

• A. $50 \,Hz$
• B. $60 \,Hz$
• C. $80 \,Hz$
• D. $100 \,Hz$

Answer 1

Answer: (C)

With $dc : P = \frac{V^2}{R} $
$\Rightarrow R = \frac{(10)^2 \times 5}{10} = 5\,\Omega$;
With $ac : P = \frac{V^2_{rms}R}{Z^2} $
$\Rightarrow Z^2 = \frac{(10)^2 \times 5}{10} = 50\,\Omega^2$
Also $Z^2 = R^2 + 4\pi^2 v^2 L^2$
$\Rightarrow 50 = (5)^2 + 4(3.14)^2 v^2 ( 10 \times 10^{-3})^2$
$ \Rightarrow v = 80\,Hz$