First slide

Phasors and Phasor Diagrams

Question

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

NA

Solution

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

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