A series LCR circuit is connected to a source of alternating e.m.f. of 50 V. The potential difference across inductor and capacitor is 80 V and 50 V respectively. The potential difference across the resistor is

Step-by-step solution

In a series LCR circuit, the relationship between the applied voltage V and the voltages across the resistor V_R , inductor V_L , and capacitor V_C is given by: V = V_R^2 + (V_L - V_C)^2 Given: V = 50 V V_L = 80 V V_C = 50 V Substituting the values into the formula: 50 = V_R^2 + (80 - 50)^2 50^2 = V_R^2 + 30^2 2500 = V_R^2 + 900 V_R^2 = 2500 - 900 = 1600 V_R = 40 V Answer: 40 V