In a series LCR circuit, the resonance frequency is $f$. If the capacitance is made $4C$ and the inductance is made $L/4$, the new resonance frequency will be:

Solution

1. The resonance frequency is $f=1/(2\pi \sqrt{LC})$.
2. The new values are $L^{\prime }=L/4$ and $C^{\prime }=4C$.
3. The new product is $$\begin{array}{rl}{L}^{\prime }{C}^{\prime }& =(L/4)\times (4C)\\ & =LC\end{array}$$.
4. The new frequency is $$\begin{array}{rl}{f}^{\prime }& =1/(2\pi \sqrt{L^{\prime }{C}^{\prime }})\\ & =1/(2\pi \sqrt{LC})\\ & =f\end{array}$$.
5. Hence the answer is (B).