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:
$X_L = 2 \pi f L$
$X_C = \frac{1}{2 \pi f C}$ (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:
$C= \frac{1}{4 \pi^2 f^2 L}= \frac{1}{4 \pi^2 (1040 Hz)^2 (0.024 H)}=9.8 \cdot 10^{-8} F=98 nF$