A capacitor, resistor of 5 Ω and an inductor of 50 mH are in series with an a.c. source marked 100 V, 50 Hz. It is found that the voltage is in phase with the current. Calculate the capacitance of the capacitor and the impedance of the circuit.

Solution

Resistance, R = 5 Ω
Inductor, I = 50 mH
Rms voltage, V_rms = 100 V
Frequency of a.c. supply, f = 50 Hz

Since the voltage is in phase with the current, therefore, it is a case of resonance.

The circuit is purely resistive.

So, impedance, Z = R = 5 Ω.

Again,

f = \frac{1}{2 π \sqrt{LC}} \Rightarrow C = \frac{1}{4 π^{2} {Lf}^{2}}

C = \frac{49}{4 \times 484 \times 50 \times 10^{- 3} \times 50 \times 50} F

= \frac{49}{4 \times 484 \times 125} F = 2.02 \times 10^{- 4} F

which, is the required capacitance of the circuit.

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Electrostatic Potential And Capacitance

A capacitor, resistor of 5 Ω and an inductor of 50 mH are in series with an a.c. source marked 100 V, 50 Hz. It is found that the voltage is in phase with the current. Calculate the capacitance of the capacitor and the impedance of the circuit.

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