Question

To receive AM radio, you want an RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed 3.83 µH inductor connected to a variable capacitor. What range of capacitance (in nF) is needed? smallest and largest value

Answer 1

In RLC circuit the frequency of the circuit is also known as resonance frequency of the circuit

It is calculated by

$f = \frac{1}{2\pi}\sqrt{\frac{1}{LC}}$

now for the maximum value of the capacitance we will use minimum frequency as they depends inversely on each other

$500* 10^3 = \frac{1}{2\pi}\sqrt{\frac{1}{3.83* 10^{-6}*C}}$

$1.01 * 10^{-13} = 3.83 * 10^{-6} * C$

$C = 2.65 * 10^{-8} farad$

Now for minimum value of the capacitance

$1650* 10^3 = \frac{1}{2\pi}\sqrt{\frac{1}{3.83* 10^{-6}*C}}$

$9.30 * 10^{-15} = 3.83 * 10^{-6} * C$

$C = 2.43 * 10^{-9} farad$

So above is the values of maximum and minimum capacitance