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=(1)/(2 \pi √(LC))`

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

By rearranging the equation, we get:

`C=(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=(1)/((2 \pi (1010 Hz))^2 (0.021 H))=1.18 \cdot 10^(-6) C=1.18 \mu C`