An alternating voltage of 200 V is applied across a series combination of a resistor, an inductor, and a capacitor. If the voltage drop across the resistor is 100 V and the voltage across the capacitor is 50 V , determine the voltage across the inductor.

Step-by-step solution

In a series RLC circuit, the applied alternating voltage V is given by the phasor sum of the voltages across the resistor, inductor, and capacitor: V^2 = V_R^2 + (V_L - V_C)^2 Substituting the given values V = 200 V , V_R = 100 V , and V_C = 50 V : (200)^2 = (100)^2 + (V_L - 50)^2 40000 = 10000 + (V_L - 50)^2 (V_L - 50)^2 = 30000 V_L - 50 = 100 3 V_L = 50 100 3 Since the RMS voltage across the inductor must be positive, we take the positive root: V_L = 50 + 100 3 = 50(2 3 + 1) V Answer: 50(2 3 + 1) V