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  4. In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

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Q. In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

JamiaJamia 2007

Solution:

In 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 $ or $ LC= $ constant $ \therefore $ $ {{L}_{1}}{{C}_{1}}={{L}_{2}}{{C}_{2}} $ $ \Rightarrow $ $ L\times C={{L}_{2}}\times 2C $ $ \Rightarrow $ $ {{L}_{2}}=\frac{L}{2} $