Question

The inductor in the RLC tuning circuit of an AM radio has a value of 9 mH. What should be the value of the variable capacitor, in picofarads, in the circuit to tune the radio to 94 kHz

Answer 1

We are asked to determine the capacitance of an RLC circuit given the frequency. To do that we will use the following formula:

`C=(1)/(4\pi^2f^2L)`

Where:

`\begin{gathered} C=\text{ capacitance} \\ f=\text{ frequency} \\ L=\text{ inductance} \end{gathered}`

Now, We plug in the values:

`C=(1)/(4\pi^2(94*10^3Hz)^2(9*10^(-3)H))`

Now, we solve the operations:

`C=3.19*10^(-10)F`

The capacitance is 3.19x10^-10 farads. In Picofarads this is equivalent to:

`C=0.0319pF`