Question

What capacitor in series with a 100 ω resistor and a 21 mh inductor will give a resonance frequency of 1010 hz ?

Answer 1

The resonant frequency in a RLC circuit is given by

$f=\frac{1}{2 \pi \sqrt{LC}}$

where L is the inductance and C the capacitance of the circuit.

By rearranging the equation, we get:

$C=\frac{1}{(2 \pi f)^2 L}$

and by substituting the inductance of the circuit, $L=21 mH=0.021 H$ and the resonant frequency, $f=1010 Hz$, we find the value of the capacitance we have to add:

$C=\frac{1}{(2 \pi (1010 Hz))^2 (0.021 H)}=1.18 \cdot 10^{-6} C=1.18 \mu C$