Question

In the given circuit, assume that the ammeter and voltmeter are ideal and $R=3\Omega ,X_L=7\Omega ,X_C=3\Omega$.
If the reading of $V_1$ is $a\sqrt{b}$ volt, then find $(a+b)$

Answer 1

Answer: 69

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}=5\Omega$
$i_{\max }=\frac{200}{5}=40A$
But wire hot instrument reads always rms value, so
$i=\frac{40}{\sqrt{2}}=20\sqrt{2}A$
$V_1=i_{\text{rms }}\times \sqrt{R^2+X_L^2}$
$=20\sqrt{2}\times \sqrt{29\times 2}$
$=40\sqrt{29}V$