A 4.00 -pF parallel plate capacitor has a potential difference of 10.0 V across it. The plates

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A 4.00 -pF parallel plate capacitor has a potential...

A 4.00 -pF parallel plate capacitor has a potential difference of $10.0 \mathrm{~V}$ across it. The plates are $3.00 \mathrm{~mm}$ apart, and the space between them contains air. a) What is the charge on the capacitor? b) How much energy is stored in the capacitor? c) What is the area of the plates? d) What would the capacitance of this capacitor be if the space between the plates were filled with polystyrene?

A 4.00 -pF parallel plate capacitor has a potential difference of $10.0 \mathrm{~V}$ across it. The plates are $3.00 \mathrm{~mm}$ apart, and the space between them contains air.
a) What is the charge on the capacitor?
b) How much energy is stored in the capacitor?
c) What is the area of the plates?
d) What would the capacitance of this capacitor be if the space between the plates were filled with polystyrene?

Key Concepts

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by a distance. The capacitance of this configuration is determined by its geometry and the permittivity of the dielectric material between the plates. The ideal formula for a parallel plate capacitor, C = ??A/d, illustrates how capacitance increases with larger plate areas and decreases with greater separation distance.

Dielectric Materials

Dielectric materials are insulating substances that, when placed between the plates of a capacitor, affect its capacitance. Introducing a dielectric increases the capacitor’s ability to store charge by reducing the effective electric field, which in turn increases the effective permittivity of the material between the plates. This effect is quantified by the dielectric constant (?), where the new capacitance becomes C = ???A/d. Different materials, such as air or polystyrene, have different dielectric constants, altering the performance of the capacitor.

Geometry of Capacitors

The geometry of a capacitor, particularly the area of the plates and the distance between them, plays a crucial role in determining its capacitance. In a parallel plate configuration, a larger plate area allows for more charge to be stored, while a smaller separation distance increases the influence of the electric field, thereby increasing the capacitance. The relationship C = ??A/d encapsulates this dependency on physical dimensions.

Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge per unit voltage. In a capacitor, capacitance is defined by the relationship Q = CV, where Q is the charge stored and V is the potential difference across the plates. It depends on the physical attributes of the device, such as the area of the plates, the distance between them, and the properties of the dielectric material between the plates.

Energy Storage in Capacitors

Capacitors store energy in the electric field created between their plates. The energy stored in a capacitor can be calculated using the formula U = ½CV², where U is the energy, C is the capacitance, and V is the voltage across the capacitor. This concept is important not only in theoretical studies but also in practical applications like power supply smoothing and energy transfer circuits.

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