Question

The self-inductance of a choke coil is $10mH$. When it is connected with a $10V$ 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. $50Hz$
• B. $60Hz$
• C. $80Hz$
• D. $100Hz$

Answer 1

Answer: (C)

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