When the rms voltages V L ,   V C and V R are measured respectively across the inductor L , the…

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 LCR circuit connected to an AC source, it is found that the ratio V L : V C : V R =1:2:3. If the rms voltage of the AC source is 100 V, then V R is close to :
  1. 50 V
  2. 70 V
  3. 100 V
  4. 90 V

Solution

V L : V C : V R =1:2:3

V rms =100 V then V R =?



Let V L =x, then V C =2x and V R =3x

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

Asked in: JEE Main 2014 (09 Apr Online)

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