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In the given circuit the readings of voltmeters $V_1$ and $V_2$ are 300 volts each. The readings of the voltmeter $V_3$ and ammeter A are respectively
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A
100 V, 2.0 A
B
150 V, 2.2 A
C
220 V, 2.2 A
D
220 V, 2.0 A
Detailed Solution
The circuit is a series LCR circuit across a 220 V, 50 Hz source, with $V_1$ across L, $V_2$ across C and $V_3$ across R = 100 $\Omega$.
$V_L = V_C = 300$ V. The voltages across L and C are $180^\circ$ out of phase, so they cancel: $V_L - V_C = 0$. The circuit is at resonance.
Source voltage: $V = \sqrt{V_R^2 + (V_L - V_C)^2} = V_R$
So $V_3 = V_R = 220$ V
At resonance the impedance is Z = R, so the current is $I = \frac{V}{R} = \frac{220}{100} = 2.2$ A
The readings are 220 V and 2.2 A.
$V_L = V_C = 300$ V. The voltages across L and C are $180^\circ$ out of phase, so they cancel: $V_L - V_C = 0$. The circuit is at resonance.
Source voltage: $V = \sqrt{V_R^2 + (V_L - V_C)^2} = V_R$
So $V_3 = V_R = 220$ V
At resonance the impedance is Z = R, so the current is $I = \frac{V}{R} = \frac{220}{100} = 2.2$ A
The readings are 220 V and 2.2 A.