Question

The AM band extends from approximately 500 kHz to 1,600 kHz. If a 2.1-4 inductor is used in a tuning circuit for a radio, what are the extremes that a capacitor must reach in order to cover the complete band of frequencies?

Answer 1

The range of capacitance needed to cover the complete AM band of frequencies from 500 kHz to 1600 kHz can be calculated using the formula for resonant frequency of an RLC circuit.

Step-by-step explanation:

The range of frequencies in the AM band is from 500 kHz to 1600 kHz. In order to cover this entire range, the tuning circuit must have a variable capacitor that can reach the extremes of this frequency range. Using the formula for resonant frequency of an RLC circuit, we can calculate the range of capacitance required.

For the lower frequency, 500 kHz, the formula is:

f = 1 / (2π√(LC))

Substituting the given values of inductance (2.1-4) and frequency (500 kHz), we can solve for capacitance:

500,000 = 1 / (2π√((2.1-4)(C)))

C = 1 / ((2π(500,000))2 * (2.1-4))

Similarly, for the higher frequency of 1600 kHz, the formula becomes:

1600,000 = 1 / (2π√((2.1-4)(C)))

C = 1 / ((2π(1600,000))2 * (2.1-4))

Therefore, the range of capacitance needed to cover the complete band of frequencies is calculated by subtracting the value of capacitance at 500 kHz from the value of capacitance at 1600 kHz.