Question

In an $LC$ circuit, $L=40\text{mH}$ and $C=100$$\mu F$. If a voltage $V\left(t\right)=10\sin \left(314t\right)$ is applied across the circuit, the current flowing through it is given as:

• A. $\text{0.52 cos 314 t}$
• B. $\text{10 cos 314 t}$
• C. $\text{5.2 cos 314 t}$
• D. $\text{0.52 sin 314 t}$

Answer 1

The correct option is A $\text{0.52 cos 314 t}$

Given, Inductance, $L=40\text{mH}$
Capacitance, $C=100\mu \text{F}$
impedance, $Z=X_C-X_L$

$\Rightarrow Z=\frac{1}{\omega C}-\omega L(\because X_c=\frac{1}{\omega C}\text{and}{X}_L=\omega L)$

$=\frac{1}{314\times 100\times {10}^{-6}}-314\times 40\times {10}^{-3}$

$=19.28\Omega$

For capacitive circuit, current leads the voltage by $\frac{\pi }{2}$, so

Current, $i=\frac{V_0}{Z}\sin (\omega t+\pi /2)$
$\Rightarrow i=\frac{10}{19.28}\cos \omega t=0.52\cos \left(314t\right)$

Hence, $\left(A\right)$ is the correct answer.