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 tha

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 ​ 100 = ( 3 x ) 2 + ( 2 x − x ) 2 ​ 100 = 10 x 2 ​ x = 10 ​ 100 ​ = 10 10 ​ ∴ V R ​ = 3 x = 30 10 ​ ≈ 90 V

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