Answer to Question #99089 in Electric Circuits for JOSIAH KARAINE KITOITOY

Question

5. A radio transmitter transmits a signal of 1MHz range. Which are the five possible selections of capacitor and inductor for capture this signal?

Answer 1

A radio receiver receives at a resonant frequency. The resonant frequency in terms of capacity and inductance is

$$f_r=\frac{1}{2\pi\sqrt{LC}}.$$

Hence:

$$L=\frac{1}{4\pi^2f_r^2C}=\frac{2.533\cdot10^{-14}}{C}.$$

Use this relation:

$C=350\text{ pF},\space L=7.237\cdot10^{-5}\text{ H};\\ C=350\text{ nF},\space L=7.237\cdot10^{-8}\text{ H};\\ C=350\space\mu\text{F},\space L=7.237\cdot10^{-11}\text{ H};\\ C=2\text{ pF},\space L=0.01267\text{ H};\\ C=5\text{ pF},\space L=5.066\cdot10^{-3}\text{ H}.$