Predict/Calculate A parallel-plate capacitor has plates with...

Predict/Calculate A parallel-plate capacitor has plates with an area of 0.012 $\mathrm{m}^{2}$ and a separation of 0.88 $\mathrm{mm} .$ The space between the plates is filled with a dielectric whose dielectric constant is $2.0 .$ (a) What is the potential difference between the plates when the charge on the capacitor plates is 4.7$\mu \mathrm{C} ?$ (b) Will your answer to part (a) increase, decrease, or stay the same if the dielectric constant is increased? Explain. (c) Calculate the potential difference for the case where the dielectric constant is 4.0.

Predict/Calculate A parallel-plate capacitor has plates with an area of 0.012 $\mathrm{m}^{2}$ and a separation of 0.88 $\mathrm{mm} .$ The space between
the plates is filled with a dielectric whose dielectric constant is $2.0 .$
(a) What is the potential difference between the plates when the charge on the capacitor plates is 4.7$\mu \mathrm{C} ?$ (b) Will your answer to
part (a) increase, decrease, or stay the same if the dielectric constant is increased? Explain. (c) Calculate the potential difference
for the case where the dielectric constant is 4.0.

Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a fixed distance, creating an electric field between them. Its design is simple and is used to illustrate key properties of capacitance where the area of the plates and their separation determine the ability to store charge.

Capacitance

Capacitance is a measure of a capacitor's ability to store electrical charge per unit potential difference. It is defined as the charge stored divided by the voltage across the capacitor. In a parallel-plate capacitor, the capacitance is proportional to the plate area and the dielectric constant and inversely proportional to the separation between the plates.

Dielectric

A dielectric is an insulating material placed between the plates of a capacitor to enhance its capacitance. When a dielectric is introduced, it reduces the effective electric field within the capacitor, which allows more charge to be stored for a given potential difference.

Dielectric Constant

The dielectric constant, or relative permittivity, is a property of a material that indicates how much it can increase a capacitor's capacitance compared to a vacuum. A higher dielectric constant means a greater ability of the material to reduce the electric field and thereby increase the capacitance.

Charge-Voltage-Capacitance Relationship

The fundamental relationship V = Q/C links the charge on a capacitor (Q), its voltage (V), and its capacitance (C). This equation shows that, for a fixed charge, an increase in capacitance (such as by using a material with a larger dielectric constant) results in a decrease in the potential difference across the capacitor.

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