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,
$tan 60 = \frac{X_{L}}{R} \Rightarrow X_{L} = \sqrt{3} R$
For CR circuit
$tan 60 = \frac{X_{C}}{R} \Rightarrow X_{C} = \sqrt{3} R$ $ \, \, ⇒ \text{X}_{\text{L}} = \text{X}_{\text{C}} = \sqrt{3} \text{R}$
$\text{I}_{\text{rms}} = \frac{\text{V}_{\text{rms}}}{R} = \frac{\text{200}}{\text{100}} = \text{2 Amp}$
$\text{P} = \text{I}^{2} \text{R} = 4 \times \text{100} = \text{400 Watt}$