Question

An ac voltmeter connected between points $A$ and $B$ in the circuit below reads $36V$. If it is connected between $A$ and $C$, the reading is $39V$. The reading when it is connected between $B$ and $D$ is $25V$. What will the voltmeter read when it is connected between $A$ and $D$?) Assume that the voltmeter reads true rms voltage values and that the source generated a pure ac.)

• A. $\sqrt{481}V$
• B. $31V$
• C. $61V$
• D. $\sqrt{3361}V$

Answer 1

The correct option is A $\sqrt{481}V$

$V_L=36.....\left(1\right)$
$V_L^2+V_R^2=(39{)}^2....(2)$
$V_R^2+V_C^2=(25{)}^2.....(3)$
by $\left(1\right)$ and $\left(2\right)$
$V_R=15....\left(4\right)$
By $\left(3\right)$ and $\left(4\right)$
$V_C=20$
By $\left(1\right),\left(4\right)$ and $\left(5\right)$
$V_{AD}=\sqrt{V_R^2+(V_L-V_C{)}^2}$
$=\sqrt{481}V$.