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.
