| Direction: Q.26 to Q.30 |
| When the frequency of AC supply is such that the inductive reactance and capacitive reactance become equal, the impedance of the series LCR circuit is equal to the ohmic resistance in the circuit. Such a series LCR circuit is known as resonant series LCR circuit and the frequency of the AC supply is known as resonant frequency. |
| Resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit. We cannot have resonance in a RL or RC circuit. |
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| A series LCR circuit with \[L=0.12\text{ }H,\text{ }C=480\text{ }nF,\text{ }R=23\,\Omega \]is connected to a 230 V variable frequency supply. |
| Based on the above information, answer the following questions. |
A) 222.32 Hz
B) 550.52 Hz
C) 663.48 Hz
D) 770 Hz
Correct Answer: C
Solution :
(c) 663.48 Hz Here, \[L=0.12\,H,C=480\,nF=480\times {{10}^{-9}}F\] \[R=23\,\Omega ,\,V=230\,V\] \[{{V}_{0}}=\sqrt{2}\times 230=325.22\,V\] \[{{l}_{0}}=\frac{{{V}_{0}}}{\sqrt{{{R}^{2}}+{{\left( \omega L-\frac{1}{\omega C} \right)}^{2}}}}\] At resonance, \[\omega L-\frac{1}{\omega C}=0\] \[\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{0.12\times 480\times {{10}^{9}}}}=4166.67\,\,rad\,{{s}^{-1}}\]\[{{v}_{R}}=\frac{4166.67}{2\times 3.14}=663.48\,Hz\]
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