A parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. Half

step 1 Hi, everybody. So what is the capsence of a combination? How much energy is stored? And if we re

A parallel-plate capacitor is made from two plates 12.0 cm...

A parallel-plate capacitor is made from two plates 12.0 $\mathrm{cm}$ on each side and 4.50 $\mathrm{mm}$ apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas' of dielectric constant 3.40 (Fig. P24.72). An 18.0-V battery is connected across the plates. (a) What is the capacitance of this combination? (Hint: Can you think of this capacitor as equivalent to two capacitors in parallel? (b) How much energy is stored in the capacitor? (c) If we remove the Plexiglas' but change nothing else, how much energy will be stored in the capacitor?

A parallel-plate capacitor is made from two plates 12.0 $\mathrm{cm}$ on each side and
4.50 $\mathrm{mm}$ apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas' of dielectric constant 3.40 (Fig. P24.72). An 18.0-V battery is connected across the plates. (a) What is the capacitance of this combination? (Hint: Can you think of this capacitor as equivalent to two capacitors in parallel? (b) How much energy is stored in the capacitor? (c) If we remove the Plexiglas' but change nothing else, how much energy will be stored in the capacitor?

Key Concepts

Parallel?Plate Capacitor

A parallel?plate capacitor consists of two conductive plates separated by a distance. Its capacitance depends on the area of the plates, the separation between them, and the material between the plates. It is a fundamental configuration in electromagnetism that stores electrical energy in the electric field created between the plates.

Dielectric Materials

Dielectric materials are insulating substances placed between the plates of a capacitor. They increase the capacitance by reducing the effective electric field, which allows more charge to be stored for the same applied voltage. The effect of a dielectric is characterized by its dielectric constant, a dimensionless number that signifies how much the dielectric increases the capacitance relative to a vacuum.

Composite Capacitor Configurations

In situations where different regions between the capacitor plates are filled with different materials (or one region is filled and another isn’t), the overall capacitor can be viewed as a combination of capacitors. These capacitors may be arranged in series or in parallel based on how the materials are distributed. This approach allows one to compute an equivalent capacitance by treating the mixed configuration as a composite of simpler capacitors.

Energy Storage in Capacitors

A capacitor stores energy in the electric field established between its plates. The energy stored in a capacitor is typically calculated using the formula U = 1/2 CV², where C is the capacitance and V is the voltage across the plates. Changes in capacitance, such as those due to the introduction or removal of a dielectric material, directly impact the amount of energy stored for a given potential difference.

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