First slide

Phasors and Phasor Diagrams

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

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

$Z = \sqrt{(R)^{2} + {(X_{L} - X_{C})}^{2}}$
$R = 10 Ω, X_{L} = ωL = 2000 \times 5 \times 10^{- 3} = 10 Ω$
$X_{C} = \frac{1}{ωC} = \frac{1}{2000 \times 50 \times 10^{- 6}} = 10 Ω, i.e., Z = 10 Ω$
$\Rightarrow Z = \sqrt{10^{2} + (10 - 10)^{2}} = 10 Ω$
Maximum current, $i_{0} = \frac{V_{0}}{Z} = \frac{20}{10} = 2 A$
Hence, $i_{rms} = \frac{2}{\sqrt{2}} = 1 .41 A$
and $V_{rms} = 4 \times 1 .41 = 5 .64 V$

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