The variable capacitance of an old radio tuner consists of...

The variable capacitance of an old radio tuner consists of four plates connected together placed alternately between four other plates, also connected together (Fig. $19-62$ ). Each plate is separated from its neighbor by 1.5 $\mathrm{mm}$ of air. One set of plates can move so that the area of overlap of each plate varies from 2.0 $\mathrm{cm}^{2}$ to $9.5 \mathrm{cm}^{2} .$ (a) Are these seven capacitors connected in series or in parallel? (b) Determine the range of capacitance values.

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Key Concepts

Series and Parallel Capacitor Configurations

Capacitors can be arranged in series or parallel, with each arrangement affecting the overall capacitance differently. In series configurations, the reciprocal of the total capacitance is the sum of the reciprocals of the individual capacitances, which generally results in a smaller net value, whereas in parallel configurations, the capacitances add directly, yielding a higher combined capacitance.

Variable Capacitors

Variable capacitors are devices that allow the adjustment of capacitance by mechanically changing parameters such as the overlapping area between the plates or the separation distance. They are critical in applications like tuning circuits in radios where varying the capacitance can change the frequency of oscillation.

Capacitance

Capacitance is the ability of a system to store electric charge per unit voltage and is determined by the geometrical configuration of the conductors as well as the intervening medium. The ideal equation for a parallel-plate capacitor illustrates its dependence on the plate area, the separation distance, and the dielectric constant of the medium between the plates.

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