Question

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 :

• A. 4L
• B. 2L
• C. L/2
• D. L/4

Answer 1

The correct option is C L/2

$\text{Resonant frequency,}{f}_r=\frac{1}{2\pi \sqrt{LC}}$

$\text{As the frequency is unchanged so}{f}_r=f_r^{\prime }$

$LC=L^{\prime }{C}^{\prime }=L^{\prime }\left(2C\right)$

$L^{\prime }=\frac{L}{2}$