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 the ideal ammeter will be:

• A. $1A$
• B. $2A$
• C. $\sqrt{2}A$
• D. $\frac{1}{\sqrt{2}}A$

Answer 1

The correct option is B $2A$

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 correct option is B.