Question

For the given AC LCR circuit, at a particular frequency of the AC source, the expression for current $\left(i\right)$ as a function of time $\left(t\right)$ will be -

• A. $i=4\sin (\omega t+8^{\circ })$
• B. $i=4\sin (\omega t-8^{\circ })$
• C. $i=2\sin (\omega t-8^{\circ })$
• D. $i=2\sin (\omega t+8^{\circ })$

Answer 1

The correct option is C $i=2\sin (\omega t-8^{\circ })$


$\tan \varphi =\frac{X_L-X_C}{R}=\frac{10-6}{3}=\frac{4}{3}$

$\Rightarrow \varphi ={53}^{\circ }$

$\Rightarrow$ Voltage lead the current by ${53}^{\circ }$ as $X_L>X_C$

So, current,

$i=\frac{V_0}{Z}\sin (\omega t+{45}^{\circ }-{53}^{\circ })$

$\Rightarrow i=\frac{10}{\sqrt{3^2+(10-6{)}^2}}\sin (\omega t-8^{\circ })$

$\Rightarrow i=2\sin (\omega t-8^{\circ })$

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