An electronics hobbyist is building a radio set to receive the AM band, with fre

Question

An electronics hobbyist is building a radio set to receive the AM band, with frequencies from520 kHz to 1500 kHz . The antenna, which also serves as the inductor in an LC circuit, has an inductance of 283 H . She needs to add a variable capacitor whose capacitance she can adjust to tune the radio.

Part A

What is the minimum capacitance the capacitor must have?

Express your answer to two significant figures and include the appropriate units.

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Part B

What is the maximum capacitance the capacitor must have?

Express your answer to two significant figures and include the appropriate units.

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An electronics hobbyist is building a radio set to receive the AM band, with frequencies from520 kHz to 1500 kHz . The antenna, which also serves as the inductor in an LC circuit, has an inductance of 283 H . She needs to add a variable capacitor whose capacitance she can adjust to tune the radio.

Part A

What is the minimum capacitance the capacitor must have?

Express your answer to two significant figures and include the appropriate units.

Cmin =

SubmitMy AnswersGive Up

Part B

What is the maximum capacitance the capacitor must have?

Express your answer to two significant figures and include the appropriate units.

Cmax =

SubmitMy AnswersGive Up

Explanation / Answer

here ,

as the frequency is in the range f = 520 kHz to 1500 kHz

inductance , L = 283 uH

part A) for the minimum capacitance ,

f = 1500 kHz

f = 1/(2pi*sqrt(L*C))

1500 *10^3 = 1/( 2*pi*sqrt(283 *10^-6 * C ))

solving for C

C = 3.98 *10^-11 F

the mimimum capacitance is 3.98 *10^-11 F

part B)

for the maximum capacitance ,

f = 520 kHz

f = 1/(2pi*sqrt(L*C))

520 *10^3 = 1/( 2*pi*sqrt(283 *10^-6 * C ))

solving for C

C = 3.31 *10^-10 F

the maximum capacitance is 3.31 *10^-10 F

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