Question

A series RC circuit has R = $\frac{125}{\sqrt{3}}\ \Omega$, C = $\frac{40}{\pi}\ \mu F$, and f = 100 Hz. Find phase difference between current and voltage.}

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Hint:

In RC circuits, current leads voltage.

Answer 1

The Correct Option is C

Step 1: Angular frequency: \[ \omega = 2\pi f = 200\pi \]
Step 2: Capacitive reactance: \[ X_C = \frac{1}{\omega C} = \frac{1}{200\pi \cdot \frac{40}{\pi}\times 10^{-6}} \]
Step 3: \[ X_C = \frac{1}{200 \cdot 40 \times 10^{-6}} = \frac{1}{0.008} = 125\ \Omega \]
Step 4: Phase angle in RC circuit: \[ \tan\phi = \frac{X_C}{R} \]
Step 5: \[ \tan\phi = \frac{125}{125/\sqrt{3}} = \sqrt{3} \Rightarrow \phi = 60^\circ \]