In A Series R-C circuit, V = 100 V and . Find The Current In The Circuit And The Voltage Across The Capacitor And The Resistor. Is The Algebraic Sum Of These Voltages More Than The Source Voltage? If Yes, Resolve The Paradox.

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Question

In a series R-C circuit, V = 100 V and . Find the current in the circuit and the voltage across the capacitor and the resistor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.

diffcult

Solution

Correct option is

0.25 A, 100 V, 7.5 V

The capacitor reactive of the circuit is

.

The impedance of the given R-C circuit is

.

The (rms) current in the circuit is

.

The (rms) voltage across the capacitor is

.

and the across the resistor is

.

The sum of these is 100 V + 7.5 V = 107.5 V, which is greater than the source voltage (100 V).

This is because the two voltages are not in phase, they are mutually perpendicular to each other.

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