First slide

Phasors and Phasor Diagrams

Question

A coil has an inductance of 0.7 H and is joined in series with a resistance of $220 Ω .$ When an AC e.m.f. of 220 V 50 Hz is applied to it, find the wattless component of current in the circuit is

Moderate

A

0.2 A
B

0.4 A
C

0.5 A
D

0.7 A

Solution

$X_{L} = ωL = 2 πfL = 220 Ω$
$ϕ = \tan^{- 1} (\frac{X_{L}}{R}) = \tan^{- 1} \frac{220}{220} = 45^{\circ}$
$I = \frac{E}{\sqrt{R^{2} + X_{L}^{2}}} = \frac{220}{\sqrt{(220)^{2} + (220)^{2}}} = \frac{1}{\sqrt{2}}$
Wattless component of current $= Isinϕ$
$= \frac{1}{\sqrt{2}} \cdot \sin 45^{\circ} = 0 .5 A$

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