Question

A 220 V A.C supply is connected between points A and B as shown in figure what will be the potential difference V across the capacitor?

• A. 220 V
• B. 110 V
• C. 0
• D. \(220\sqrt2\ V\)

Answer 1

The Correct Option is D

When an A.C. supply is connected to a capacitor, the voltage across the capacitor is out of phase with the current. The voltage across the capacitor will be the peak voltage of the AC supply. The RMS value of the AC supply is 220 V. The peak voltage \( V_{\text{peak}} \) is related to the RMS value \( V_{\text{rms}} \) by the formula: \[ V_{\text{peak}} = V_{\text{rms}} \times \sqrt{2} \] Substituting the given value of \( V_{\text{rms}} = 220 \, \text{V} \): \[ V_{\text{peak}} = 220 \times \sqrt{2} = 220\sqrt{2} \, \text{V} \] Thus, the potential difference across the capacitor is \( 220\sqrt{2} \, \text{V} \).

The correct answer is (D) : \(220\sqrt2\ V\).

Answer 2

In an AC circuit, when a capacitor is connected to an alternating current (AC) supply, the potential difference across the capacitor leads the current by 90°. This is a typical property of capacitive reactance in AC circuits. Given that the supply voltage is \( V_{\text{supply}} = 220 \, \text{V} \), this is the root-mean-square (RMS) voltage of the AC supply. The peak voltage \( V_{\text{peak}} \) is related to the RMS voltage by: \[ V_{\text{peak}} = V_{\text{RMS}} \times \sqrt{2} \] Substituting the given RMS voltage \( V_{\text{RMS}} = 220 \, \text{V} \): \[ V_{\text{peak}} = 220 \times \sqrt{2} = 220\sqrt{2} \, \text{V} \] Thus, the peak potential difference across the capacitor is \( 220\sqrt{2} \, \text{V} \).