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

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

It is calculated by

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

Now for minimum value of the capacitance

So above is the values of maximum and minimum capacitance

it is a negative acceleration