Question

# In the circuit shown in the figure, the $$AC$$ source gives a voltage $$V=20 \cos(2000t)$$. Neglecting source resistance, the voltmeter and ammeter reading will be:

A
0 V,0.47 A
B
1.68 V,0.47 A
C
0 V,1.4 A
D
5.6 V,1.4 A

Solution

## The correct option is D $$5.6\ V, 1.4\ A$$We know$$Z=\sqrt{(R)^2+(X_L-X_C)^2}$$Here $$R=10\Omega,\ X_L=\omega L=2000\times5\times10^{-3}=10\ \Omega$$$$X_C=\dfrac{1}{\omega C}=\dfrac{1}{2000\times50\times10^{-6}}=10\ \Omega$$So,$$Z=\sqrt{(10)^2}$$$$Z=10\ \Omega$$Maximum current $$i_)=\dfrac{V_0}{Z}=\dfrac{20}{10}=2\ A$$Hence,$$I_{rms}=\dfrac{2}{\sqrt2}=1.4\ A$$$$V_{rms}=4\times1.4=5.6\ V$$PhysicsNCERTStandard XII

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