Electro Magnetic Induction And Alternating Currents Question 146
Question: An LCR series circuit with a resistance of 100 ohm is connected to an ac source of 200 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by $ 60^{o} $ . When only the inductor is removed the current leads the voltage by $ 60^{o} $ . The average power dissipated is
Options:
A) 50 W
B) 100 W
C) 200 W
D) 400 W
Show Answer
Answer:
Correct Answer: D
Solution:
$ \tan \varphi =\frac{X_{L}}{R}=\frac{X_{C}}{R}\Rightarrow \tan 60^{o}=\frac{X_{L}}{R}=\frac{X_{C}}{R} $
$ \Rightarrow X_{L}=X_{C}=\sqrt{3}\ R $
i.e. $ Z=\sqrt{R^{2}+{{(X_{L}-X_{C})}^{2}}}=R $
So average power $ P=\frac{V^{2}}{R}=\frac{200\times 200}{100} $ = 400W
