A series LCR circuit has initial components L , C , R and a quality factor Q₀ . The capacitance is replaced by a new capacitor of capacitance 16C . The inductance is simultaneously changed such that the resonance frequency of the circuit remains completely unchanged. If the resistance R is kept constant, the new quality factor of the circuit will be :

Step-by-step solution

The resonance frequency of a series LCR circuit is given by ₀ = 1 LC . Since the resonance frequency remains unchanged, the product of inductance and capacitance must remain constant: L' C' = L C Given the new capacitance C' = 16C , we can find the new inductance L' : L' (16C) = L C L' = L 16 The quality factor of a series LCR circuit is given by Q = 1 R L C . The initial quality factor is Q₀ = 1 R L C . The new quality factor Q' is: Q' = 1 R L' C' Substituting the values of L' and C' : Q' = 1 R L/16 16C = 1 R L 25