Electro Magnetic Induction And Alternating Currents Question 130
Question: In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $ E=E_{0}\cos (\omega t) $ applied to the circuit. The power consumed in the circuit is [MP PMT 1997]
Options:
A) $ \frac{E_{0}^{2}}{R} $
B) $ \frac{E_{0}^{2}}{2R} $
C) $ \frac{E_{0}^{2}}{4R} $
D) $ \frac{E_{0}^{2}}{8R} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ P=E_{rms}i_{rms}\cos \varphi =\frac{E_{0}}{\sqrt{2}}\times \frac{i_{0}}{\sqrt{2}}\times \frac{R}{Z} $
Þ $ \frac{E_{0}}{\sqrt{2}}\times \frac{E_{0}}{Z\sqrt{2}}\times \frac{R}{Z} $
$ \Rightarrow P=\frac{E_{0}^{2}R}{2Z^{2}} $ Given $ X_{L}=R $ so, $ Z=\sqrt{2}R $
$ \Rightarrow ,P=\frac{E_{0}^{2}}{4R} $
