Resonance frequency of L-C-R series AC circuit is f0 . Now the capacitance is made 4 times, then the new resonance frequency will become

Question

Resonance frequency of L-C-R series AC circuit is f0 . Now the capacitance is made 4 times, then the new resonance frequency will become (A)  ( f0/ 4)  (B) 2 f0 (C)  f0 (D)  ( f0/ 2)

Tardigrade Admin · Accepted Answer

In l-C-R series circuit, resonance occurs when

X_{L} = X_{C}

or

ω L = \frac{1}{ω C}

or

ω^{2} = \frac{1}{L C}

or

ω = \frac{1}{L C}

\Rightarrow 2 π f_{0} = \frac{1}{L C}

f_{0} = \frac{1}{2 π L C}

∴ f_{0} \propto \frac{1}{C}

When capacitance of the circuit is made 4 times, Iet its resonant frequency become

f_{0}^{'}

.

∴ \frac{f _{0}^{'}}{f _{0}} = \frac{C}{4 C}

or

f_{0}^{'} = \frac{f _{0}}{2}

Q. Resonance frequency of L-C-R series AC circuit is $f_{0}$ . Now the capacitance is made 4 times, then the new resonance frequency will become

$\frac{f _{0}}{4}$

2 $f_{0}$

$f_{0}$

$\frac{f _{0}}{2}$

Q. Resonance frequency of L-C-R series AC circuit is f0​ . Now the capacitance is made 4 times, then the new resonance frequency will become

4f0​​

2f0​

f0​

2f0​​

Q. Resonance frequency of L-C-R series AC circuit is $f_{0}$ . Now the capacitance is made 4 times, then the new resonance frequency will become

$\frac{f _{0}}{4}$

2 $f_{0}$

$f_{0}$

$\frac{f _{0}}{2}$