JEE MainPhysicsAlternating Current
A series LCR circuit is tuned to a resonant frequency f₀ . If an identical inductor is connected in parallel to the original inductor, what modification should be made to the capacitor to ensure the resonant frequency remains unchanged?
Options
- AAn identical capacitor should be connected in parallel with the original capacitor.
- BAn identical capacitor should be connected in series with the original capacitor.
- CA capacitor of half the original capacitance should be connected in parallel with the original capacitor.
- DA capacitor of half the original capacitance should be connected in series with the original capacitor.
Correct answer
A. An identical capacitor should be connected in parallel with the original capacitor.
Step-by-step solution
The resonant frequency of a series LCR circuit is given by f₀ = 1 2 LC . When an identical inductor is connected in parallel, the equivalent inductance becomes L' = L L L + L = L 2 . To keep the resonant frequency unchanged, the product of equivalent inductance and equivalent capacitance must remain constant. Therefore, L' C' = LC ( L 2 ) C' = LC C' = 2C . To double the capacitance, an identical capacitor must be connected in parallel with the original capacitor, since for parallel capacitors C_ eq = C₁ + C₂ = C +