Question

A $400$$\Omega$ resistor and $6\mu F$ capacitor are connected in parallel to a source of $V_{rms}=220V$ and angular frequency $360rad/s$. Find the current in the resistor and capacitor.

• A. 0.55 A, 0.475 A
• B. 0.65 A, 0.726 A
• C. 0.55 A, 0.176 A
• D. none of these

Answer 1

The correct option is A 0.55 A, 0.475 A

$\frac{1}{X_C}=C\omega =6\times {10}^{-6}\times 360=2.16\times {10}^{-3}$
$\frac{1}{Z}=\sqrt{\frac{1}{R^2}+\left(C\omega {)}^2\right)}$
$\frac{1}{Z}=$$\sqrt{{\left(\frac{1}{400}\right)}^2+(2.16\times {10}^{-3}{)}^2}$
$I_{net}=220\times \frac{1}{Z}=220\times {10}^{-3}\times 3.3=0.726;$
$I_R=\frac{220}{400}=0.55A$
$I_C=\sqrt{I_{net}^2-I_R^2}=\sqrt{(0.726{)}^2-(0.55{)}^2}=0.475A$