A series LCR circuit is connected to an AC source of 120 V and 60 Hz . The value of resistance R in the circuit is 100 .A voltmeter reads the voltage across R as 50 V , across the inductor as 132 V and across the capacitor as 70 6.6 ~V . The value of inductance and capacitance in the circuit is:

Step-by-step solution

Given V_ R = 50 V , V_ L = 132 V , V_ C = 70 6.6 V 10.6 V , and R = 100 . The current in the series LCR circuit is I = V_ R R = 50 100 = 0.5 A . The inductive reactance X_ L is given by X_ L = V_ L I = 132 0.5 = 264 . Since X_ L = 2 f L , where f = 60 Hz , we have L = 264 2 60 = 264 377 0.7 H . The capacitive reactance X_ C is given by X_ C = V_ C I = 70 / 6.6 0.5 = 140 6.6 21.21 . Since X_ C = 1 2 f C , we have C = 1 2 60 (140 / 6.6) = 6.6 2 60 140 = 6.6 52778 1.25 10⁻⁴ F = 125 F . Comparing these values with the