Question

In an LC circuit, the angular frequency is ω = √1/LC. Explain why an LC circuit with a larger inductance or a larger capacitance will oscillate more slowly. Make your explanation based on physics, not mathematics.

Answer 1

Consider the freely oscillationg LC circuit

we know the reactance across the inductor and capacitor are X_L ,X_C

X_L = W*L

X_C =1/(W*C)

if the X_L = X_C then it attains the resonance frequency which is given by

1/(W*C) = W*L

W^2 = 1/(L*C)

W = 1/sqrt(L*C)

W is resonance frequency

W is low if the values of the incuctance and the capacitance values are large

as the denomenator increases the fraction value decrease so the frequency decreases means oscillates more slowly.