Question:medium

A diode is connected to a $220$ V (rms) ac source in series with a capacitor as shown in the diagram. Find the voltage (rms) across the capacitor.



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The diode charges the capacitor to the peak of the ac input and then blocks discharge. Peak voltage is \(\sqrt{2}\) times the rms value.
Updated On: Oct 21, 2026
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Solution and Explanation

Step 1: Follow the circuit during one cycle:
The diode symbol points towards the capacitor, so it conducts from the source to the capacitor. The capacitor has no resistor across it.

Step 2: First positive half cycle:
As the input rises, the diode conducts and the capacitor voltage follows the input. The capacitor reaches the maximum input value $V_0$ at the top of the wave.

Step 3: After the peak:
The input now falls below the capacitor voltage. The diode becomes reverse biased and acts as an open switch, so the charge stays on the plates. The same thing happens in the negative half cycle, since the diode blocks current in that direction.
So the capacitor stays at $V_0$ and is a steady dc level.

Step 4: Convert the 220 V rms to the peak:
The quoted 220 V is an rms value. The peak of a sine wave is $\sqrt{2}$ times the rms:
\[ V_0 = 220 \times 1.414 = 311.1\ \text{V} \]

Final Answer:
The capacitor holds the peak voltage, about 311 V. \[ \boxed{V_C \approx 311\ \text{V}} \]
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