Variable Capacitor

An RLC series circuit is built with a variable capacitor. By what factor does the resonant frequency of the ci?

An RLC series circuit is built with a variable capacitor. By what factor does the resonant frequency of the circuit change when the area of the capacitor is increased by a factor of 12?

Parallel plate cap
C = ε₀εr(A/d) in Farads
ε₀ is 8.8542e-12 F/m
εr is dielectric constant (vacuum = 1)
A and d are area of plate in m² and separation in m

increase the area by 12 and the capacitance increases by the same factor.

Resonant frequency:
f = 1/(2π√(LC))
f = 1/(2π√(12*LC))
f = (1/√12)(1/(2π√(LC)))

resonant frequency changes by a factor of (1/√12) or 0.289

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