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jim12glo
An RLC circuit is used to tune a radio set to receive NOUN RADIO broadcasting at 105.9MHz in the FM band. The resistance and the inductance of the circuit of the radio set are 12Ω and 1.4 μH respectively. What capacitance should the circuit have?
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It can be assumed that the series resistance of the inductance in the resonant circuit is very small compared with L/C. In that case the resonant frequency of the tuned circuit is given by \[f _{o}=\frac{1}{2 \pi \sqrt{LC}}..........(1)\] and, by rearranging (1) \[C=\frac{1}{4 \pi ^{2} L f _{o}^{2}}...........(2)\] where \[L=1.4 \times 10^{-6}\] and \[f _{o}^{2}=105.9^{2} \times 10^{12}\] Now just plug the values into equation (2) and calculate the required value of C.
Will it matter if the inductor is not resistance free? Will series resonant frequency be different if we had taken a inductor with some resistance?
@Diwaka On the condition that the series resistance of the inductance in the resonant circuit is very small compared with L/C, there is negligible difference in the result of the calculations if it is assumed that that inductor has zero resistance.