question_answer

An inductance of 1 mH and a capacitance of 10 h F are connected in a circuit. The angular frequency of circuit will be

A) \[\text{1}{{0}^{\text{3}}}\text{ rad}/\text{s}\]                                  

B)  \[\text{1}{{0}^{4}}\text{ rad}/\text{s}\]

C) \[\text{1}{{0}^{2}}\text{ rad}/\text{s}\]               

D)  \[\text{1}{{0}^{5}}\text{ rad}/\text{s}\]

Correct Answer: B

Solution :

                 At resonance, inductive reactance \[({{X}_{L}})\] is equal to capacitive reactance \[({{X}_{C}})\]. Therefore,                                 \[{{X}_{L}}={{X}_{C}}\]                                 \[\omega L=\frac{1}{\omega C}\Rightarrow \omega =\frac{1}{\sqrt{LC}}\]                 Given,   \[L=1\,mH=1\times {{10}^{-3}}H\],                                 \[C=10\,\mu F=10\times {{10}^{-6}}F\]                 \[\therefore \]  \[\omega =\frac{1}{\sqrt{{{10}^{-3}}\times 10\times {{10}^{-6}}}}\] \[\Rightarrow \]               \[\omega ={{10}^{4}}rad/s\]