Answered

Join IDNLearn.com and start exploring the answers to your most pressing questions. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.

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

Sagot :

Given:

The inductance is I = 10 mH

The frequency is f = 97 kHz

Required:

Value of capacitor in picofarads.

Explanation:

In order to tune the radio, the condition is

[tex]X_L=X_c[/tex]

Here, X_L is the inductive reactance and

X_C is the capacitive reactance.

The capacitance can be calculated as

[tex]\begin{gathered} 2\pi fL=\frac{1}{2\pi fC} \\ C=\frac{1}{(2\pi f)^2L} \\ =\frac{1}{(2\times3.14\times97\times10^3)^2\times10\times10^{-3}} \\ =2.69\text{ }\times10^{-10}\text{ F}\times\frac{10^{12}\text{ pF}}{1\text{ F}} \\ =269\text{ pF} \end{gathered}[/tex]

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

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.