A circuit with a resistor, inductor, and capacitor in series has a resonant frequency of fo Hz. If all the component values are now doubled, the new resonant frequency is

A circuit with a resistor, inductor, and capacitor in series has a resonant frequency of fo Hz. If all the component values are now doubled, the new resonant frequency is

Right Answer is:

fo/2

SOLUTION

The resonant frequency for series R-L-C circuit is given by

${f_o} = \dfrac{1}{{2\pi \sqrt {LC} }}$——(1)

Now inductor and capacitor value is doubled the above equation becomes

${f_1} = \dfrac{1}{{2\pi \sqrt {2L \times 2C} }}$——(2)

Dividing equation 2 from 1 we get

$\begin{array}{l}\dfrac{{{f_1}}}{{{f_o}}} = \dfrac{1}{{4\pi \sqrt {LC} }} \times 2\pi \sqrt {LC} \\\\{f_1} = \dfrac{{{f_o}}}{2}\end{array}$

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