Current and ResistanceCurrent and Resistance

February 22, 2006February 22, 2006

Notes Notes

New topic today – Current and New topic today – Current and ResistanceResistance

Exam – Friday – March 3 Through Exam – Friday – March 3 Through Chapter 27.Chapter 27.

No quiz on Friday.No quiz on Friday.Watch for new WebAssign.Watch for new WebAssign.

A capacitor is constructed from two square plates of sides ℓ and separation d. A material of dielectric constant κ is inserted a distance x into the capacitor, as shown in the figure. Assume that d is much smaller than x. (a) Find the equivalent capacitance of the device. (b) Calculate the energy stored in the capacitor, letting ΔV represent the potential difference. (c) Find the direction and magnitude of the force exerted on the dielectric, assuming a constant potential difference ΔV. Ignore friction. (d) Obtain a numerical value for the force assuming that ℓ = 5.00 cm, ΔV = 2 000 V, d = 2.00 mm, and the dielectric is glass (κ = 4.50).

Each capacitor in the combination shown in Figure P26.49 has a breakdown voltage of 15.0 V. What is the breakdown voltage of the combination?

Current and Resistance

Physical Resistors

What Happens?

“+”

“+”

“+”

“+”

IN TRUTH, THE ELECTRONS

ARE ACTUALLY MOVING THE

OTHER WAY!-

-

DEFINITION

Current is the motion of CHARGE through a circuit. Physically, it is electrons that move but …

We define current as the motion of POSITIVE charge! (Blame you know who!)

Conducting material

Q,t

Conducting material

Q,t

dt

dqi

ort

Qi

CURRENT

UNITS

A current of one coulomb per second is defined as ONE AMPERE.

A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent?

ANOTHER DEFINITION

A

I

area

currentJ

Figure P27.8 represents a section of a circular conductor of non-uniform diameter carrying a current of 5.00 A. The radius of cross section A1 is 0.400 cm. (a) What is the magnitude of the current density across A1? (b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor at A2?

Ohm A particular object will resist the flow of current.

It is found that for any conducting object, the current is proportional to the applied voltage.

STATEMENT: V=IR R is called the resistance of

the object. An object that allows a

current flow of one ampere when one volt is applied to it has a resistance of one OHM.

Graph

A DIODE

Resistance Varies with Applied Voltage (actually with current)

Let’s look at the atomic level ..

Conduction is via electrons. They are weak and small and don’t exercise

much. Positive charge is big and strong and doesn’t

intimidate easily. It’s an ugly situation … something like ……

-

+

Consider a metal conductor

So far, we have said that a metal is an equipotential because no charges were moving. Hence, no electric field in the metal You can move a charge freely in the metal BECAUSE there

is no electric field.

NOW we have a current. This can only happen if we allow an electric field to push

the charges. Thus, the metal is NO LONGER A TRUE

EQUIPOTENTIAL. But almost …. as we shall see in the next chapter.

l

VV ab E

The Current

Electrons are going the other way. They probably follow a path like …

Average “drift”speed - vd

Notation

vd average drift velocity of the electron n number of electrons (mobile) per unit

volume. t interval of time x average distance the electron moves in

time t. Q total amount of CHARGE that goes

through a surface of the conductor in time t.

dvJ ne

nevA

IJ

enAvt

QI

etnAvQ

davg

davg

d

)(

Reference

The average drift velocity of an electron is about 10-4 m/s

Conductivity

In metals, the bigger the electric field at a point, the bigger the current density.

EJ is the conductivity of the material.

=(1/) is the resistivity of the material

Going to the usual limit …

JdAI

anddA

dIJ

Example

A cylindrical conductor of radius R has a current density given by

(a) J0 (constant)

(b) r

Find the total current in each case.

)(1 00 TT

Range of and

Ye old RESISTANCE

IRVVA

lR

IA

lV

A

I

l

VE

El

VEJ

ElV

11

Additional Topics

Power Micro basis of conduction.