Question

The instantaneous values of current and voltage in an AC circuit are $i=100\sin 314t$ amp and $e=200\sin (314t+\frac{\pi }{3})V$ respectively. If the resistance is $1\Omega$, then the reactance of the circuit will be:

• A. $\sqrt{3}\Omega$
• B. $100\sqrt{3}\Omega$
• C. $-200\sqrt{3}\Omega$
• D. $-200/\sqrt{3}\Omega$

Answer 1

The correct option is A $\sqrt{3}\Omega$

We have, $V_0=i_{0}Z$
$\Rightarrow 200=100Z$
$Z=2\Omega$
So, the impedance of the circuit
$Z^2=R^2+X_L^2$
$\Rightarrow (2{)}^2=(1{)}^2+X_L^2$
$X_L=\sqrt{3}\Omega$