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Question 22

In an $$LCR$$ circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220 V and 100 Hz is connected to it as shown?

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Solution

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Using AC voltage phasor relationship: $$V_{\text{rms}} = \sqrt{V_R^2 + (V_L - V_C)^2}$$

Identifying condition from $$V_L = V_C$$: $$V_L - V_C = 0 \implies \text{Circuit is at resonance}$$

$$220 = \sqrt{V_R^2 + (300 - 300)^2} \implies V_R = 220\text{ V}$$

$$I_{\text{rms}} = \frac{V_R}{R} = \frac{220}{100} = 2.2\text{ A}$$

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