1. Tardigrade
  2. Question
  3. Physics
  4. 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:

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Q. 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:

JEE MainJEE Main 2014Alternating Current

Solution:

$I=\frac{V_{rms}}{Z}=\frac{V_{rms}}{\sqrt{R^{2}+\left(X_{L}-X_{C}\right)}^{2}}=\frac{100}{\sqrt{9x^{2}+x^{2}}}=\frac{100}{\sqrt{10x^{2}}}$
Since $V_{L} : V_{C} : V_{R} = 1 : 2 : 3$
$X_{L}=X_{C} : X_{R}=1 : 2 : 3$
$=x : 2x : 3x$
now $V_{R}=I\left(3x\right)$
$=\frac{100}{\sqrt{10x^{2}}}.3x$
$\approx94.87\,V$