Electrical Engineering Question

Given circuit,

Now,

Voltage $v_s\left(t\right)=35\sin \left(4000t\right)$,

here,

$$\begin{gathered} V=35\angle 0° \\ \omega =4000 \text{rad/s} \end{gathered}$$

Calculating the values of reactances,

Inductive reactance,

 $\begin{array}{rcl}{X}_L& =& \omega L\\ & =& 4000\times 2.5\times {10}^{-3}\\ & =& 10 \text{Ω}\end{array}$

Capacitive reactance,

$\begin{array}{rcl}{X}_C& =& \frac{1}{\omega C}\\ & =& \frac{1}{4000\times 12.5\times {10}^{-6}}\\ & =& 20 \text{Ω}\end{array}$

Now,

Drawing the equivalent circuit in phasor form,

here,

$20 \text{Ω}\parallel -j20 \text{Ω}$

Thus the equivalent resistance is,

$\begin{array}{rcl}{R}_{eq}& =& \frac{20\times -j20}{20\times -j20}\\ & =& \left(10-j10\right) \text{Ω}\end{array}$