First slide

Electrical Resonance series circuit

Question

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

Moderate

A

0V, 0.47A
B

1.68V, 0.47A
C

0V, 1.4 A
D

5.6V, 1.4 A

Solution

$Z = \sqrt{{(R)}^{2} + {(X_{L} - X_{C})}^{2};} \begin{array}{l} R = 10 Ω, X_{L} = ωL = 2000 \times 5 \times 10^{- 3} = 10 Ω \\ X_{C} = \frac{1}{ωC} = \frac{1}{2000 \times 50 \times 10^{- 6}} = 10 Ω i.e. Z = 10 Ω \end{array} Maximum current i_{0} = \frac{V_{0}}{Z} = \frac{20}{10} = 2 A Hence i_{rms} = \frac{2}{\sqrt{2}} = 1 .4 A$

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