Question

For an L-R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf $ E={{E}_{0}}\cos (\omega t) $ is applied to the circuit. Then, the power consumed in the circuit is

• A. $ \frac{{{E}_{0}}}{R} $
• B. $ \frac{E_{0}^{2}}{4R} $
• C. $ \frac{4R}{{{E}_{0}}} $
• D. $ \frac{R}{{{E}_{0}}} $

Answer 1

Answer: (B)

For $L - R$ conbination, given,
$ X _{ L }= R $
Impedance $Z =\sqrt{ R ^{2}+ R ^{2}}$
$ =\sqrt{2} R $
Power consumed $=\left(\frac{ V _{ rms }}{ Z }\right)^{2} R $
$=\left(\frac{ E _{0} / \sqrt{2}}{\sqrt{2} R }\right)^{2} R =\frac{ E _{0}^{2}}{4 R } $