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  • Current through an AC series L-C-R circuit is 2 A if operated at resonant frequency, and 1 A if operated at 50% less than resonant frequency. The current (in A) if the frequency is 100% more than t

Current through an AC series L-C-R circuit is 2 A if operated at resonant frequency, and 1 A if operated at 50% less than resonant frequency. The current (in A) if the frequency is 100% more than the resonant frequency, is:

Option: 1

\sqrt{2}


Option: 2

1


Option: 3

\sqrt{3}


Option: 4

Data insufficient


Answers (1)

best_answer

At resonance, \mathrm{X}_{\mathrm{C}}=\mathrm{X}_{\mathrm{L}}
If \omega is reduced to half,
\begin{aligned} & \mathrm{X}_{\mathrm{C}}^{\prime}=2 \mathrm{X}_{\mathrm{C}} \quad\left[\text { as } \mathrm{X}_{\mathrm{C}} \propto \frac{1}{\omega}\right] \\ & \mathrm{X}_{\mathrm{L}}^{\prime}=\frac{\mathrm{X}_{\mathrm{L}}}{2} \\ & \text { [as } \mathrm{X}_{\mathrm{L}} \propto \omega \text { ] } \\ & \end{aligned}
and
If \omegais made two times,X_C^{\prime}=\frac{X_C}{2} and X_L^{\prime}=2 X_L i.e., value of \mathrm{Z} will remain unchanged current should be \mathrm{1 \mathrm{~A}.}

Posted by

sudhir.kumar

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