CircuitsResistors, Capacitors and Inductors

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Resistors

Capacitors

Inductors

CircuitsResistors, Capacitors and Inductors

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CircuitsResistors, Capacitors and Inductors

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Resistors slow down the electrons

I

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Resistors slow down the electrons

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CircuitsResistors, Capacitors and Inductors

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In most instances, the voltage across a piece of material is proportional to the current that flows through it

This is known as Ohm’s law and is usually written as

The constant of proportionality is called resistance, R, and has units of Ohms (Ω)

IRV

In a circuit diagram we draw resistance like this

R

CircuitsResistors, Capacitors and Inductors

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For many materials, the resistance is proportional to the length of the resistor and inversely proportional to the cross-sectional area

Table 28.2 in the text gives resistivity for some materials

The constant of proportionality is called resistivity, ρ, and is different for different materials

A

LR

As length increases, the electrons are blocked for a longer time, slowing them down even more. Thus, the current is smaller and the resistance is greater

As area increases, more electrons pass through it. Thus, the current is greater and the resistance is smaller

CircuitsResistors, Capacitors and Inductors

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Power is defined as the change in energy per unit time

In the case of electric potential energy, we can write

The power may be written in different forms using Ohm’s law

IVt

qV

t

UP

IVP

RIP 2

R

VP

2

CircuitsResistors, Capacitors and Inductors

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E

Δs

dkV 2

kE 2

EdV

+σ

CircuitsResistors, Capacitors and Inductors

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V=0

V=4πkσd

-σ

d

E

d

A

kd

A

dk

A

V

QC 044

+σ

CircuitsResistors, Capacitors and Inductors

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-σ

E0

Ed

V=4πkσd0/κ

d

V=0

d0

0

0

EEEE d

0EE

+σ

CircuitsResistors, Capacitors and Inductors

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Capacitors store the electrons

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CircuitsResistors, Capacitors and Inductors

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A capacitor is two conductors of equal but opposite charge separated by a dielectric.

A dielectric is a substance made up of stationary dipoles.

The capacitance of a capacitor is given by the equation.

V

QC

Q is magnitude of the charge of one of the conductors.

V is the magnitude of the difference in potential between them.

The capacitance depends only on the geometry (shape and size of the capacitor, not on Q or V because they are proportional to each other.

CircuitsResistors, Capacitors and Inductors

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For any capacitor, the electric potential energy is given by

22

2

1

2

1

2

1CV

C

QQVU

But where is that energy found?

For a parallel plate capacitor…

dAECVU 20

2

2

1

2

1

202

1

VolumeE

Uue

This is the electrostatic field energy density.

The energy lies in the electric field!

CircuitsResistors, Capacitors and Inductors

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Inductors create magnetic fields

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