A series L-C-R circuit is connected to an AC source of 220 ~V and 50 ~Hz shown in figure. If the readings of the three voltmeters V₁, V₂ and V₃ are 65 ~V , 415 ~V and 204 ~V respectively, the value of inductance and capacitance will be

Step-by-step solution

In a series LCR circuit, the voltage across the resistor is V_R = V₁ = 65 V , the voltage across the capacitor is V_C = V₂ = 415 V , and the voltage across the inductor is V_L = V₃ = 204 V . The current I in the circuit is given by I = V_R R . However, the resistance R is not given. We use the source voltage V = 220 V . In a series LCR circuit, V = V_R^2 + (V_L - V_C)^2 . Substituting the given values: V = 65^2 + (204 - 415)^2 = 65^2 + (-211)^2 = 4225 + 44521 = 48746 220.78 V . This matches the source voltage of 22