An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $45^{\circ}$,…

An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $45^{\circ}$, then $\left(\tan 45^{\circ}=1\right)$
  1. $X_L=X_C-R$
  2. $X_L=X_C+R$
  3. $X_C=\sqrt{X_L^2+R^2}$
  4. $\mathrm{X}_{\mathrm{L}}=\sqrt{\mathrm{X}_{\mathrm{C}}^2+\mathrm{R}^2}$

Solution

The phase between the voltage and the current is given as $\begin{array}{ll} & \tan \phi=\frac{X_L-X_C}{R} \\ \therefore \quad & \tan 45^{\circ}=\frac{X_L-X_C}{R} \\ \therefore \quad & 1=\frac{X_L-X_C}{R} \\ \therefore \quad & R=X_L-X_C \\ \therefore \quad & X_L=X_C+R \end{array}$

Asked in: MHT CET 2023 (14 May Shift 1)

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