First slide

AC Circuits

Question

The instantaneous values of current and voltage in an ac circuit are $i = 100 \sin 314 t amp$ and $e = 200 \sin (314 t + π / 3) V$ respectively. If the resistance is 1 $Ω$ then the reactance of the circuit will be

Moderate

A

$- 200 \sqrt{3} Ω$
B

$\sqrt{3} Ω$
C

$- 200 / \sqrt{3} Ω$
D

$100 \sqrt{3} Ω$

Solution

$V_{0} = i_{0} Z \Rightarrow 200 = 100 Z \Rightarrow Z = 2 Ω$
Also $Z^{2} = R^{2} + X_{L}^{2} \Rightarrow {(2)}^{2} = {(1)}^{2} + X_{L}^{2} \Rightarrow X_{L} = \sqrt{3} Ω$

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