Question

An RLC series circuit has:
- Resistance $ R = 150\, \Omega $
- Capacitance $ C = 20\, \mu\text{F} $
- Inductance $ L = 500\, \text{mH} $
- AC voltage $ V = 100\, \text{V} $
- Angular frequency $ \omega = 400\, \text{rad/s} $
Find the phase angle $ \phi $ between current and voltage.

• A. \( \tan^{-1}(0.8) \)
• B. \( \tan^{-1}(0.25) \)
• C. \( \tan^{-1}(0.6) \)
• D. \( \tan^{-1}(0.5) \)

Hint:

Use \( \tan \phi = \frac{X_L - X_C}{R} \) to find phase angle in an RLC circuit.

Answer 1

The Correct Option is D

Inductive reactance: \[ X_L = \omega L = 400 \cdot 0.5 = 200\, \Omega \] Capacitive reactance: \[ X_C = \frac{1}{\omega C} = \frac{1}{400 \cdot 20 \times 10^{-6}} = \frac{1}{0.008} = 125\, \Omega \] Net reactance: \[ X = X_L - X_C = 200 - 125 = 75\, \Omega \] Phase angle: \[ \tan \phi = \frac{X}{R} = \frac{75}{150} = 0.5 \Rightarrow \phi = \tan^{-1}(0.5) \]