Question

For RLC circuit shown below, the rms voltage across capacitor is

• A. \(200\angle -90^\circ V\)
• B. \(100\angle -90^\circ V\)
• C. \(400\angle -90^\circ V\)
• D. \(400\angle 90^\circ V\)

Hint:

At resonance, impedance = resistance only.

Answer 1

The Correct Option is C

Concept: Voltage across capacitor: \[ V_C = I X_C \]

Step 1: Given values \[ X_L = 20\Omega,\quad X_C = 20\Omega,\quad R = 10\Omega \]

Step 2: Resonance condition \[ X_L = X_C \Rightarrow \text{resonance} \]

Step 3: Impedance \[ Z = R = 10\Omega \]

Step 4: Current \[ I = \frac{200}{10} = 20A \]

Step 5: Voltage across capacitor \[ V_C = I X_C = 20 \times 20 = 400V \] Phase is \(-90^\circ\).

Final Answer: \[ \boxed{400\angle -90^\circ V} \]