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

$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=5 \,\Omega$
$i_{\max }=\frac{200}{5}=40 \,A$
But wire hot instrument reads always rms value, so
$i=\frac{40}{\sqrt{2}}=20 \sqrt{2}\, A $
$V_{1}=i_{ \text{rms }} \times \sqrt{R^{2}+X_{L}^{2}}$
$=20 \sqrt{2} \times \sqrt{29 \times 2}$
$=40 \sqrt{29} \,V$