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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

Respuesta :

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

It is calculated by

[tex]f = \frac{1}{2\pi}\sqrt{\frac{1}{LC}}[/tex]

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

[tex]500* 10^3 = \frac{1}{2\pi}\sqrt{\frac{1}{3.83* 10^{-6}*C}}[/tex]

[tex]1.01 * 10^{-13} = 3.83 * 10^{-6} * C[/tex]

[tex]C = 2.65 * 10^{-8} farad[/tex]

Now for minimum value of the capacitance

[tex]1650* 10^3 = \frac{1}{2\pi}\sqrt{\frac{1}{3.83* 10^{-6}*C}}[/tex]

[tex]9.30 * 10^{-15} = 3.83 * 10^{-6} * C[/tex]

[tex]C = 2.43 * 10^{-9} farad[/tex]

So above is the values of maximum and minimum capacitance

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