Question

What is the resonance frequency if the capacitor value is doubled and the inductor value is halved? express your answer with the appropriate units?

Answer 1

In an LC circuit, the resonance frequency is given by

`\omega_0 = (1)/( √(LC) )`
where L is the value of the inductance and C is the value of the capacitance.
If we double the capacitance: C'=2C and the inductance is halved: L'=L/2, the new resonance frequency is

`\omega' = (1)/( √(L'C') )= \frac{1}{ \sqrt{ (L)/(2) \cdot 2C } }= (1)/( √(LC) )=\omega_0`
so, the new frequency of resonance is equal to the original value, so it didn't change.