Final answer:
The variable capacitor in a superheterodyne receiver is used for b. tuning the local oscillator, which is fundamental in setting the resonant frequency to pick up the desired radio signal.
Step-by-step explanation:
In a superheterodyne receiver without an RF amplifier, the input to the mixer stage has a variable capacitor in parallel with an inductance. The variable capacitor is primarily used for tuning the local oscillator. This tuning is essential for selecting the desired radio frequency to which the receiver will be set. Along with the inductance, it forms an LC circuit which determines the resonant frequency of the receiver circuit. The resonant frequency is matched to the frequency of the desired radio station, enabling the receiver to pick up the signal while filtering out other frequencies. Variable capacitors provide a practical means to adjust the resonant frequency allowing for the selection of different stations.