Q. The self inductance of a choke coils is $10\ mH$. 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) 50 $Hz$
B) 60 $Hz$
C) 80 $Hz$
D) 100 $Hz$
Explanation
(c) With dc : $P = \frac{V^{2}}{R} \Rightarrow R = \frac{(10)^{2}}{20} = 5\Omega;$
With ac : $P = \frac{V_{rms}^{2}R}{Z^{2}} \Rightarrow Z^{2} = \frac{(10)^{2} \times 5}{10} = 50\ \Omega^{2}$
Also $Z^{2} = R^{2} + 4\pi^{2}v^{2}L^{2}$
$\Rightarrow 50 = (5)^{2} + 4(3.14)^{2}v^{2}\left( 10 \times 10^{- 3} \right)^{2} \Rightarrow v = 80\ Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.