Question

In the AC circuit shown, $X_L=7\Omega ,R=4\Omega and{X}_c=4\Omega .$ The reading of the ideal voltmeter $V_{2}is8\sqrt{2}$. The reading of idea voltmeter $V_1$ will be :

• A. 20 volt
• B. 7 volt
• C. 8 volt
• D. 10 volt

Answer 1

The correct option is D 10 volt

From the given figure,

Given,

$X_L=7\Omega$

$X_C=4\Omega$

$R=4\Omega$

The reading of ideal voltmeter is given by

$V_2=8\sqrt{2}V$

From Ohm's law,

$V_2=I\left(R+j{X}_C\right)$ (Capacitor and resistor are in series)

$I=\frac{V_2}{R+j{X}_C}$

$I=\frac{V_2}{\sqrt{(R{)}^2+(X_C{)}^2}}$

$I=\frac{8\sqrt{2}}{\sqrt{(4{)}^2+(4{)}^2}}$

$I=\frac{8\sqrt{2}}{4\sqrt{2}}$

$I=2A$

The voltage $V_1=IZ=I[R+j(X_L-X_C\left)\right]$

$V_1=2(4+j3)$

$V_1=2\sqrt{(4{)}^2+(3{)}^2}=2\sqrt{25}$

$V_1=2\times 5=10volt$

The correct option is D.