24.24. A parallel-plate air capacitor has a capacitance of 920 pF . The charge on each plate is

step 1 In the given problem, there is a parallel plate air capacitor whose capacitance has been given a

24.24. A parallel-plate air capacitor has a capacitance of...

24.24. A parallel-plate air capacitor has a capacitance of 920 $\mathrm{pF}$ . The charge on each plate is 2.55$\mu \mathrm{C}$ . (a) What is the potential difference between the plates? (b) If the charge is kept constant,what will be the potential difference between the plates if the sep ration is doubled? (c) How much work is required to double the separation?

Key Concepts

Work Done in Changing Capacitor Geometry

When the physical parameters of a capacitor, such as the plate separation, are changed while keeping the charge constant, the capacitance and the stored energy will change. The work done on the capacitor to change its configuration is equivalent to the change in stored electrical energy. This concept connects the mechanical work done to modify physical dimensions with the resulting electrical energy variations.

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a dielectric medium, such as air. The geometry of the capacitor directly influences its capacitance, with larger plate areas and smaller separations yielding higher capacitance. The ideal parallel-plate capacitor provides a clear model to study how physical dimensions impact electrical properties.

Energy Storage in a Capacitor

The energy stored in a capacitor is given by the formula U = 1/2 CV^2 or alternatively U = Q^2/(2C). This stored energy represents the work done to charge the capacitor and is crucial for understanding how energy changes when the capacitor's physical configuration is altered, such as when the plate separation is modified.

Capacitance

Capacitance is the measure of a capacitor's ability to store an electrical charge per unit voltage. It depends on physical factors such as the area of the plates, the separation between them, and the dielectric constant of the material between the plates. In the context of a parallel-plate capacitor, the capacitance is directly proportional to the plate area and inversely proportional to the separation distance.

Charge-Voltage Relationship

The relationship between charge, capacitance, and voltage in a capacitor is defined by the equation Q = CV, where Q is the stored charge, C is the capacitance, and V is the potential difference. This fundamental relationship shows how changes in either charge or capacitance will directly affect the voltage across the capacitor.

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