Question

In a series lrc circuit, the frequency at which the circuit is at resonance is f0. If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency?.

Answer 1

When you double capacitance and inductance, the new resonance frequency becomes halved.

What is Resonance frequency?

It is the natural frequency of an object where it tends to vibrate at a higher amplitude.

The resonance frequency of the LC series circuit is the frequency at which the capacity reactance is equal to inductive reactance.

The formula resonance frequency:

$f_{0} = \frac{1}{2\pi \sqrt{LC} }$

where;

f0 is the resonance frequency

L is the inductance

C is the capacitance

here, if the capacitance and inductance are doubled, the new resonance frequency becomes;

$f = \frac{1}{2\pi \sqrt{2L2C} }\\f = \frac{1}{2\pi \sqrt{4LC} }\\f = \frac{1}{2*2\pi \sqrt{LC} }\\f=\frac{1}{2} \frac{1}{2\pi \sqrt{LC} }\\f = \frac{1}{2} f_{0}$

Thus from the above equation for frequency,

When you double capacitance and inductance, the new resonance frequency becomes f(0) / 2.

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