First slide

Phasors and Phasor Diagrams

Question

In an ac circuit containing a resistor and an inductor connected in series, supply voltage (v) and resulting current are given by v = 100 sin 200t volt and i = 50 sin (200t - $π$ /3) Amp. Then the resistance of the resistor is

Moderate

A

$\sqrt{2} Ω$
B

$\frac{1}{2} Ω$
C

$\sqrt{3} Ω$
D

$1 Ω$

Solution

Phase difference between v and i is $ϕ = \frac{π}{3}$
$∴ \frac{X_{L}}{R} = \tan \frac{π}{3} \Rightarrow X_{L} = R \tan 60^{o} = \sqrt{3} R$
Impedance $Z = \frac{V_{rms}}{I_{rms}} = \frac{100 / \sqrt{2}}{50 / \sqrt{2}} Ω = 2 Ω$
Now, ${X_{L}}^{2} + R^{2} = Z^{2} \Rightarrow (\sqrt{3} R^{2}) + R^{2} = {(2)}^{2} \Rightarrow R = 1 Ω$

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