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 sources is 100 V , the V R is close to:

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 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 sources is 100 V , the V R is close to: (A) 50 V (B) 70 V (C) 90 V (D) 100 V

Tardigrade Admin · Accepted Answer

I=(Vrms/Z)=(Vrms/√R2+(XL-XC)2)=(100/√9x2+x2)=(100/√10x2) Since VL: VC: VR = 1: 2: 3 XL=XC: XR=1: 2: 3 =x: 2x: 3x now VR=I(3x) =(100/√10x2).3x ≈94.87 V

$50 V$

$70 V$

$90 V$

$100 V$

50V

70V

90V

100V

I=ZVrms​​=R2+(XL​−XC​)​2Vrms​​=9x2+x2​100​=10x2​100​ Since VL​:VC​:VR​=1:2:3 XL​=XC​:XR​=1:2:3 =x:2x:3x now VR​=I(3x) =10x2​100​.3x ≈94.87V

$50 V$

$70 V$

$90 V$

$100 V$