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. $100\, V$

Answer 1

Answer: (C)

$90\, V$

Answer 2

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