question_answer

In an L-C-R circuit, the capacitance is made 1/4, then what should be change in inductance, so that the circuit remains in resonance?

A)  8 times                               

B)  1/4 times

C)  c) 2 rimes                           

D)  4 times

Correct Answer: D

Solution :

                 Key Idea: In resonance condition resistance of circuit is zero. The condition for resonance is that the frequency of the applied emf should be equal to the natural frequency of the circuit when the resistance of the circuit is zero. \[\therefore \]  \[f=\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\] Given, \[{{C}_{1}}=C,{{L}_{1}}=L\]                 \[{{C}_{2}}=\frac{C}{4}\] \[\therefore \]  \[f=\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\]                 \[=\frac{1}{2\pi }\frac{1}{\sqrt{{{L}_{2}}.\frac{C}{4}}}\] \[\Rightarrow \]               \[{{L}_{2}}=4L\] Hence, inductance should be made four times.