Question

A series $LCR$ circuit with $\text{100 }\Omega$ resistance is connected to an ac source of $\text{200 V}$ with an angular frequency of ${\text{300 rad s}}^{-1}$ . If only the capacitor is removed, the current lags behind the voltage by a phase of ${\text{60}}^{{}^{\circ }}$ . If only the inductor is removed, the current leads the voltage by a phase of ${\text{60}}^{{}^{\circ }}$ . The current and the power dissipated in the circuit is

• A. $\text{3 A}$ , $\text{300 W}$
• B. $\text{5 A}$ , $\text{100 W}$
• C. $\text{4 A}$ , $\text{200 W}$
• D. $\text{2 A}$ , $\text{400 W}$

Answer 1

Answer: (D)

From given condition circuit is at resonance
For LR circuit,
$tan60=\frac{X_L}{R}\Rightarrow X_L=\sqrt{3}R$
For CR circuit
$tan60=\frac{X_C}{R}\Rightarrow X_C=\sqrt{3}R$ $\Rightarrow {\text{X}}_{\text{L}}={\text{X}}_{\text{C}}=\sqrt{3}\text{R}$
${\text{I}}_{\text{rms}}=\frac{{\text{V}}_{\text{rms}}}{R}=\frac{\text{200}}{\text{100}}=\text{2 Amp}$
$\text{P}={\text{I}}^2\text{R}=4\times \text{100}=\text{400 Watt}$