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 value in nF and largest value in nF

Answer 1

The formula for resonant frequency is:

$f_0=\frac{1}{2\pi\sqrt{LC} }$

Given information:

$f_{0\text{,small}}=500 \text{ kHz}\\f_{0\text{,large}}=1650 \text{ kHz}\\L=3.83\text{ } \mu \text{H}$

Plug in the given values to find one value of capacitance:

$500 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.645*10^{-8} \text{ F}=26.45 \text{ nF}$

Plug in the given values to find the other value of capacitance:

$1650 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.429*10^{-8} \text{ F}=2.429 \text{ nF}$

This gives a range of 2.429 nF to 26.45 nF.

With significant figures taken into account, the range of capacitance is 2.43 nF to 30 nF.

Answer 2

Answer:

The formula for resonant frequency is:

Explanation: