Question

What capacitor in series with a 100ω resistor and a 24.0 mh inductor will give a resonance frequency of 1040 hz ?

Answer 1

The resonant frequency of a RLC circuit in series is the frequency at which the inductive reactance and the capacitive reactance are equal:

`X_L = X_C`
where:

`X_L = 2 \pi f L`

`X_C = (1)/(2 \pi f C)` (1)
where
f is the frequency
L is the inductance
C is the capacitance

In our circuit, we have the inductance:

`L=24.0 mH=0.024 H`
and the resonant frequency:

`f=1040 Hz`
so we can re-arrange eq.(1) to find the capacitance of the circuit:

`C= (1)/(4 \pi^2 f^2 L)= (1)/(4 \pi^2 (1040 Hz)^2 (0.024 H))=9.8 \cdot 10^(-8) F=98 nF`