A series LCR circuit is connected to an ac source of 200 ~V , 50 ~Hz . If the current in the circuit is 4 ~A and the voltage across the capacitor is 100 ~V , then the capacitance of the capacitor is:

Step-by-step solution

The voltage across the capacitor is given by V_C = I X_C . Substituting the given values: 100 = 4 X_C X_C = 25 , The angular frequency of the ac source is: = 2 f = 2 ( 50 ) = 100 ~rad/s The capacitive reactance is X_C = 1 C . Therefore, the capacitance is: C = 1 X_C = 1 100 25 = 1 2500 ~F C = 4 10⁻⁴ ~F = 400 F Note that the source voltage ( 200 ~V ) is not required to find the capacitance since the voltage across the capacitor is already known. Answer: 400 F