MHT CET · Physics · Alternating Current
An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by \(45^{\circ}\), then \(\left(\tan 45^{\circ}=1\right)\)
- A \(X_L=X_C-R\)
- B \(X_L=X_C+R\)
- C \(X_C=\sqrt{X_L^2+R^2}\)
- D \(\mathrm{X}_{\mathrm{L}}=\sqrt{\mathrm{X}_{\mathrm{C}}^2+\mathrm{R}^2}\)
Answer & Solution
Correct Answer
(B) \(X_L=X_C+R\)
Step-by-step Solution
Detailed explanation
The phase between the voltage and the current is given as
\(
\begin{array}{ll}
& \tan \phi=\frac{X_L-X_C}{R} \\
\therefore & \tan 45^{\circ}=\frac{X_L-X_C}{R} \\
\therefore & 1=\frac{X_L-X_C}{R} \\
\therefore & R=X_L-X_C \\
\therefore & X_L=X_C+R
\end{array}
\)
\(
\begin{array}{ll}
& \tan \phi=\frac{X_L-X_C}{R} \\
\therefore & \tan 45^{\circ}=\frac{X_L-X_C}{R} \\
\therefore & 1=\frac{X_L-X_C}{R} \\
\therefore & R=X_L-X_C \\
\therefore & X_L=X_C+R
\end{array}
\)
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