When the rms voltages V L , V C and V R are measured respectively across the inductor L , the capacitor C and the resistor R in a series L C R circuit connected to an A C source, it is found that the

Question

When the rms voltages V L , V C and V R are measured respectively across the inductor L , the capacitor C and the resistor R in a series L C R circuit connected to an A C source, it is found that the ratio V L : V C : V R = 1 : 2 : 3. If the rms voltage of the A C source is 100 V , then V R is close to :

TestHub · Accepted Answer

V L : V C : V R = 1 : 2 : 3 V rms = 100 V then V R = ? Let V L = x , then V C = 2 x and V R = 3 x using V = V R 2 + ( V c − V L ) 2 1 0 0 = 3 x 2 + 2 x - x 2 1 0 0 = 1 0 x 2 x = 1 0 0 1 0 = 10 10 ∴ V R = 3 x = 30 10 ≈ 90 V

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