A) 4L
B) 2L
C) L/2
D) L/4
Correct Answer: C
Solution :
| [c] At resonance, the net reactance of an AC circuit is zero. i.e., the circuit behaves like a purely resistive circuit with resonant frequency\[\frac{1}{2\pi \sqrt{LC}}\]. |
| At the condition of resonance, |
| \[{{X}_{L}}={{X}_{C}}\] |
| Or \[\omega L=\frac{1}{\omega C}\] .(i) |
| Since, resonant frequency remains unchanged. |
| So, \[\sqrt{LC}=\]constant (\[v=\frac{1}{2\pi \sqrt{LC}}=\]constant) |
| \[\Rightarrow \] \[LC=\]constant |
| \[\therefore \] \[{{L}_{1}}{{C}_{1}}={{L}_{2}}{{C}_{2}}\] |
| \[\Rightarrow \] \[L\times C={{L}_{2}}\times 2C\] \[(\because {{L}_{1}}=L)\] |
| \[\Rightarrow \] \[{{L}_{2}}=\frac{L}{2}\] |
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