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  • In an LCR circuit contains resistance of 100 ohms and a supply of 200 volts at 300 radians angular frequency. If only capacitance is taken out from the circuit and the rest of the circuit is joined

In an LCR circuit contains resistance of 100 ohms and a supply of 200 volts at 300 radians angular frequency. If only capacitance is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by 60°. If on the other hand only inductor is taken out, the current leads by 60° with the applied voltage. The current flowing in the circuit is

Option: 1

1A


Option: 2

1.5A


Option: 3

2A


Option: 4

2.5A


Answers (1)

best_answer

According to the given question,

\mathrm{\begin{aligned} & \tan 60^{\circ}=\frac{\omega \mathrm{L}}{\mathrm{R}} \text { and } \tan 60^{\circ}=\frac{1 / \omega \mathrm{C}}{\mathrm{R}} \\ & \therefore \omega \mathrm{L}=\frac{1}{\omega \mathrm{C}} \text { (case of resonance) } \\ & \text { Now } \mathrm{Z}=\sqrt{\left[\mathrm{R}^2+\left(\omega \mathrm{L}-\frac{1}{\omega \mathrm{C}}\right)^2\right]}=\mathrm{R} \\ & \therefore \quad \mathrm{I}_{\mathrm{ms}}=\frac{\mathrm{E}_{\text {rms }}}{\mathrm{Z}}=\frac{\mathrm{E}_{\text {rms }}}{\mathrm{R}}=\frac{200 \mathrm{~V}}{100 \Omega}=2 \mathrm{amp} \end{aligned} }

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SANGALDEEP SINGH

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