Question

A capacitor of reactance \( 4 \sqrt{3} \, \Omega \) and a resistor of resistance \( 4 \, \Omega \) are connected in series with an AC source of peak value \( 8 \sqrt{2} \, \text{V} \). The power dissipation in the circuit is ___________ W.

Answer 1

Correct Answer: 4

The impedance $Z$ of the circuit is: \[ Z = \sqrt{R^2 + X_C^2} = \sqrt{4^2 + (4\sqrt{3})^2} = \sqrt{16 + 48} = \sqrt{64} = 8 \, \Omega. \] The RMS voltage is: \[ V_\text{rms} = \frac{V_\text{peak}}{\sqrt{2}} = \frac{8\sqrt{2}}{\sqrt{2}} = 8 \, \text{V}. \] The RMS current is: \[ I_\text{rms} = \frac{V_\text{rms}}{Z} = \frac{8}{8} = 1 \, \text{A}. \] Power dissipation in the resistor is: \[ P = I_\text{rms}^2 R = 1^2 \cdot 4 = 4 \, \text{W}. \]