Final answer:
The midband frequency range is where an RC coupled amplifier's gain stays constant. For an RLC circuit to receive AM radio between 500 and 1650 kHz, a range of capacitances for a fixed 1.00 µH inductor must be calculated using the resonant frequency formula.
Step-by-step explanation:
The frequency range over which the gain of an RC coupled amplifier is essentially constant is known as the midband frequency range. To calculate the range of capacitance needed for an RLC circuit to receive AM radio between 500 and 1650 kHz using a fixed 1.00 µH inductor, we use the formula for resonant frequency ω = 1 / √(LC), where L is the inductance and C is the capacitance. By rearranging this formula to solve for C and substituting the given frequencies, we can determine the required capacitance values.
For the lower frequency limit (500 kHz), a higher capacitance value is required, and for the upper-frequency limit (1650 kHz), a lower capacitance value is required. Therefore, to cover the AM radio band, a variable capacitor that can adjust between these two capacitance values is needed.