Question

The inductor in the RLC tuning circuit of an AM radio has a value of 10 mH. What should be the value of the variable capacitor, in picofarads, in the circuit to tune the radio to 97 kHz

Answer 1

Given:

The inductance is I = 10 mH

The frequency is f = 97 kHz

Required:

Value of capacitor in picofarads.

Step-by-step explanation:

In order to tune the radio, the condition is

`X_L=X_c`

Here, X_L is the inductive reactance and

X_C is the capacitive reactance.

The capacitance can be calculated as

`\begin{gathered} 2\pi fL=(1)/(2\pi fC) \\ C=(1)/((2\pi f)^2L) \\ =(1)/((2*3.14*97*10^3)^2*10*10^(-3)) \\ =2.69\text{ }*10^(-10)\text{ F}*\frac{10^(12)\text{ pF}}{1\text{ F}} \\ =269\text{ pF} \end{gathered}`

Final Answer: The value of the variable capacitor is 269 picoFarad.