Ncert Exercises & Solutions

Question 7.9:

A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 µF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

The supply frequency and the natural frequency are equal at resonance condition in the circuit.

Given Resistance of the resistor, R = 20 Ω

Given Inductance of the inductor, L = 1.5 H

Given Capacitance of the capacitor , C = 35 μF = 30 × 10 ^{– 6} F

An AC source with a voltage of V = 200 V is connected to the LCR circuit,

We know that the Impedance of the above combination can be calculated by the following relation,

$a Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$

At resonant condition in the circuit , X _L = X _C

Therefore , Z = R = 20 Ω

We know that Current in the network is given by the relation :

$à I = \frac{V}{Z} = \frac{200}{20} = 10 A$

Therefore, the average power that is being transferred to the circuit in one full cycle:

V I = 200 x 10 = 2000 W

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