First slide

AC Circuits

Question

As given in the figure, a series circuit connected across a 200 V, 60 Hz line consists of a capacitor of capacitive reactance 30ohm , a non-inductive resistor of 44 ohm , and a coil of inductive reactance 90ohm and resistance 36ohm . The power dissipated in the coil is (watt)

Moderate

Solution

$X_{C} = 30 Ω, X_{L} = 90 Ω, R = 44 + 36 = 80 Ω$
$I_{r m s} = \frac{V_{r m s}}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}$
$\begin{array}{l} \Rightarrow I_{r m s} = \frac{200}{\sqrt{(80)^{2} + (90 - 30)^{2}}} = 2 A \\ Power in coil = {I_{rms}}^{2} R_{2} = {(2)}^{2} \times 36 = 144 W \end{array}$

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