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

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Solution

Since the voltage is in phase with the current in series RLC circuit, this means the current is flowing at resonant frequency.
At resonance, Capacitive reactance is equal to inductive reactance i.e. $X_{C} = X_{L}$
Given : $R = 5 Ω$ $L = 50 m H = 0.05 H$ $f_{r} = 50 H z$
Resonant frequency is given by $f_{r} = \frac{1}{2 π \sqrt{L C}}$
$∴$ $50 = \frac{1}{2 π \sqrt{0.05 C}}$
$⟹ C = 200 μ F$
Impedance of circuit $Z = \sqrt{R^{2} + (X_{C} - X_{L})^{2}}$
$⟹ Z = R$ $(∵ X_{C} = X_{L})$
Thus $Z = 5 Ω$

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

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