1 / 16

# TOPIC 5 Capacitors and Dielectrics - PowerPoint PPT Presentation

TOPIC 5 Capacitors and Dielectrics. Capacitors. Capacitors are a means of storing electric charge (and electric energy) It takes energy to bring charge together A capacitor allows more charge to be stored for a given energy It does this by reducing the potential at which the charge is stored

Related searches for TOPIC 5 Capacitors and Dielectrics

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'TOPIC 5 Capacitors and Dielectrics' - psyche

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

TOPIC 5Capacitors and Dielectrics

• Capacitors are a means of storing electric charge (and electric energy)

• It takes energy to bring charge together

• A capacitor allows more charge to be stored for a given energy

• It does this by reducing the potential at which the charge is stored

• It can do this by bringing an opposite charge into close proximity, to reduce the overall repulsion

Capacitance (C) is charge per unit potential difference

C = Q/V

Unit is Farad (F): 1 F = 1 Coulomb/Volt

Typical capacitances measured in F (10–6 F) or pF (10–12 F)

Two plates, area A, separation d, carrying charge Q.

Gauss’s Law (using dotted Gaussian surface shown)

E A = Q/0  E = Q/0A

A parallel plate capacitor has plates with dimensions 3 cm by 4 cm, separated by 2 mm. The plates are connected across a 60 V battery. Find:

(a) the capacitance;

(b) the magnitude of charge on each plate;

(c) the energy stored in the capacitor – see later!

What is the capacitance of a long cylindrical (coaxial) cable of inner radius a, outer radius b and length L as shown?

What is the capacitance of two concentric spherical conducting shells of inner radius a and outer radius b?

Capacitors connected as shown, with terminals connected together, are said to be in parallel.

They behave as a single capacitor with effective capacitance C.

Total charge Q = Q1 + Q2 = C1V + C2V

Therefore C = Q/V = C1 + C2

Capacitors connected together as shown, sharing one common terminal, are said to be in series.

They behave as a single capacitor with effective capacitance C.

The external charge stored is Q.

The voltages across the capacitors Vi= Q/Ci must add up to V.

Therefore V = Q/C1 + Q/C2 = Q/C

If each of the individual capacitors in the network below has a capacitance C, what is the overall effective capacitance?

Adding an increment of charge dq to a capacitor requires work dW = V dq = q/C dq

This is obviously the increase in (potential) energy stored of the capacitor U

The total energy required to charge a capacitor from zero charge to Q is therefore

Since Q = CV, we can express this in other ways:

A parallel plate capacitor has plates with dimensions 3 cm by 4 cm, separated by 2 mm. The plates are connected across a 60 V battery. Find:

(a) the capacitance;

(b) the magnitude of charge on each plate;

(c) the energy stored in the capacitor – see later!

Previously:

C = 5.3 pF

Q = 3.210–10 C

The energy stored in the capacitor can also be considered as the energy stored in its electric field.

We have

For the parallel plate capacitor we also have

V = Ed and

So

But A d is the volume where the electric field exists, so the energy density is

This is a general result for the energy density in a field.

A conductor contains free charges that can move through the material.

A dielectric contains bound charges, which cannot move freely but will displace through small distances when affected by an electric field.

This leaves excess bound charges on the surface of the material.

This reduces the electric field within the bulk of the material.

The factor by which the electric field is reduced is known as the dielectric constantk (or r).

If the gap between the plates of a capacitor is filled with dielectric material, the voltage between the plates for a given charge will also be reduced by the factor k.

Since C = Q / V, this means that C is increased by k.

For the parallel plate capacitor, we therefore have

Demonstrate that the energy stored in a spherical capacitor is consistent with an energy density stored in the field of