Q. The instantaneous values of current and voltage in an ac circuit are $i = 100\sin{314\ t\ amp}$ and $e = 200\ in\ (314\ t + \pi/3)V$ respectively. If the resistance is $1\Omega$, then the reactance of the circuit will be
A) $- 200\sqrt{3}\ \Omega$
B) $\sqrt{3}\ \Omega$
C) $- 200\sqrt{3}\ \Omega$
D) $100\sqrt{3}\ \Omega$
Explanation
(b) $V_{0} = i_{0}Z \Rightarrow 200 = 100\ Z\ \Rightarrow Z = 2\Omega$
Also $Z^{2} = R^{2} + X_{L}^{2} \Rightarrow (2)^{2} = (1)^{2} + X_{L}^{2} \Rightarrow X_{L} = \sqrt{3}\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.