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An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $45^{\circ}$, then $\left(\tan 45^{\circ}=1\right)$
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2892 Upvotes
Verified Answer
The correct answer is:
$X_L=X_C+R$
The phase between the voltage and the current is given as
$$
\begin{array}{ll}
& \tan \phi=\frac{X_L-X_C}{R} \\
\therefore \quad & \tan 45^{\circ}=\frac{X_L-X_C}{R} \\
\therefore \quad & 1=\frac{X_L-X_C}{R} \\
\therefore \quad & R=X_L-X_C \\
\therefore \quad & X_L=X_C+R
\end{array}
$$
$$
\begin{array}{ll}
& \tan \phi=\frac{X_L-X_C}{R} \\
\therefore \quad & \tan 45^{\circ}=\frac{X_L-X_C}{R} \\
\therefore \quad & 1=\frac{X_L-X_C}{R} \\
\therefore \quad & R=X_L-X_C \\
\therefore \quad & X_L=X_C+R
\end{array}
$$
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