A series LCR circuit is connected to an ac source of 50 ~V , 50 ~Hz . The voltage across the inductor is 60 ~V , the voltage across the capacitor is 20 ~V , and the resistance in the circuit is 15 , . The inductance of the inductor is:

Step-by-step solution

In a series LCR circuit, the source voltage V_S is related to the voltages across the components by phasor addition: V_S^2 = V_R^2 + (V_L - V_C)^2 Substituting the given values: (50)^2 = V_R^2 + (60 - 20)^2 2500 = V_R^2 + 1600 V_R^2 = 900 V_R = 30 ~V The current in the series circuit is the same for all components and can be found using Ohm's law for the resistor: I = V_R R = 30 15 = 2 ~A Now, applying Ohm's law for the inductor: V_L = I X_L 60 = 2 X_L X_L = 30 , The angular frequency of the ac source is: = 2 f = 2