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Chapter 18: Problem 52

In your own words, explain the mechanism by which charge-storing capacity is increased by the insertion of a dielectric material within the plates of a capacitor.

Short Answer

Expert verified
Answer: Inserting a dielectric material between the plates of a capacitor increases its charge-storing capacity by increasing the permittivity (ε) of the material and reducing the net electric field between the plates due to polarization. This results in a decrease in voltage and an increase in capacitance.

Step by step solution

01

1. Understanding Capacitance

Capacitance is the ability of a capacitor to store electrical energy between two conductive plates separated by an insulating material, typically air or a vacuum. The capacitance is given by the formula C = εA/d, where C is the capacitance, ε is the permittivity of the dielectric material, A is the overlapping area of the plates, and d is the distance between the plates.
02

2. Introducing Dielectric Material

When a dielectric material is inserted between the plates of a capacitor, it replaces the air or vacuum present initially. Dielectric materials have a higher permittivity (ε) than air or vacuum, which directly affects the capacitance value in the formula C = εA/d.
03

3. Dielectric Polarization

Dielectric materials are made up of molecules with positive and negative charges. When an external electric field is applied across the capacitor plates, the dielectric material gets polarized, causing the positive and negative charges in the material to align with the electric field. This leads to an induced electric field within the material, which opposes the external electric field.
04

4. Increased Capacitance

Due to the induced electric field in the dielectric material, the net electric field between the plates decreases. As a result, the voltage across the capacitor is reduced, which is given by V = Ed, where V is the voltage, E is the electric field, and d is the distance between the plates. As capacitance is directly proportional to the charge (Q) stored and inversely proportional to the voltage (V), according to the formula C = Q/V, the decrease in voltage causes an increase in the capacitance of the capacitor.
05

5. Conclusion

In summary, when a dielectric material is inserted between the plates of a capacitor, it increases the capacitance by increasing the permittivity (ε) of the material and reducing the net electric field between the plates due to polarization. This results in a decrease in voltage and an increase in charge-storing capacity.

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Most popular questions from this chapter

Calculate the room-temperature electrical conductivity of silicon that has been doped with \(5 \times 10^{22} \mathrm{~m}^{-3}\) of boron atoms.

(a) Using the data in Figure \(18.8\), determine the values of \(\rho_{0}\) and \(a\) from Equation \(18.10\) for pure copper. Take the temperature \(T\) to be in degrees Celsius. (b) Determine the value of \(A\) in Equation \(18.11\) for nickel as an impurity in copper, using the data in Figure \(18.8\). (c) Using the results of parts (a) and (b), estimate the electrical resistivity of copper containing \(1.75\) at \(\%\) Ni at \(100^{\circ} \mathrm{C}\).

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