First slide

AC Circuits

Question

In the circuit shown below, the ac source has voltage $V = 20 \cos (ωt)$ volts with $ω$ = 2000 rad/sec. the amplitude of the current will be nearest to

Moderate

A

$2 A$
B

3.3 A
C

$2 / \sqrt{5} A$
D

$\sqrt{5} A$

Solution

$R = 6 + 4 = 10 Ω$
$X_{L} = ωL = 2000 \times 5 \times 10^{- 3} = 10 Ω$
$X_{C} = \frac{1}{ωC} = \frac{1}{2000 \times 50 \times 10^{- 6}} = 10 Ω$
$∴ Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = 10 Ω$
Amplitude of current $= i_{0} = \frac{V_{0}}{Z} = \frac{20}{10} = 2 A$

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