A resistor of 100 $\Omega$ and a capacitor of $100 / \pi\mu\text{F}$ are connected in series to a 220 V, 50 Hz a.c. supply.
- Calculate the current in the circuit.
- Calculate the (rms) voltage across the resistor and the capacitor. Do you find the algebraic sum of these voltages more than the source voltage? If yes, how do you resolve the paradox?
CBSE OUTSIDE DELHI - SET 2 CHENNAI 2015
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- Current in the circuit $\text{I} = \frac{\text{V}}{\sqrt{\text{R}^{2} + \bigg(\frac{1}{\text{C}\omega}\bigg)^{2}}}$
$ = \frac{2.2}{\sqrt{2}}\text{A} = 1.55\text{A}$
- Voltage across the resistor$ = 100\times1.55 \text{V}$
Voltage across the capacitor $ = 100\times1.55 \text{V}$
$ = 155 \text{ volt}$
Yes,
The sum of the two voltages is greater than 220 V but the voltage across the resistor and the capacitor are not in phase.
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