Question

A series LCR circuit is connected to an ac source of frequency f and a voltage v. At this frequency, reactance of the capacitor is $350$ ohm while the resistance of the circuit is $180$ ohm. Current in the circuit leads the voltage by ${54}^0$ and power dissipated in the circuit is $140$ watt, Therefore, voltage v is

• A. $250$ volt
• B. $260$ volt
• C. $270$ volt
• D. $280$ volt

Answer 1

The correct option is C $270$ volt

$\begin{array}{c}Given\\ v_e=350\Omega \\ z\cos 54=R\\ z=\frac{R}{\cos {54}^{\circ }}\\ amd\\ R=180\Omega \\ P=140W\\ I^{2}R=140\\ I=\sqrt{\frac{140}{180}}\\ Now,\\ v=Iz\\ v=\sqrt{\frac{14}{18}}\times \frac{R}{\cos 54}\\ =\sqrt{\frac{14}{18}}\times \frac{180}{\cos 54}\\ =\frac{10\sqrt{18}\times \sqrt{14}}{\cos 54}\\ =270.12V.\end{array}$