Physics ch 281

Current, Resistance, and Electromotive Force

Sections 1-5, 7

Chapter 28

Physics ch 282

Current

Movement of charges Scalar quantity Amount of charge transferred per unit time

Measured in amperes or amps 1A = 1 C/s

t

QI

Physics ch 283

Traditional current direction

Current flows in the direction that positive charge would flow.

It is impossible to experimentally determine which charges are moving.

We know that the electrons are actually moving in the opposite direction of current flow, but we keep with tradition.

Physics ch 284

Drift velocity

Speed of the moving particles. n particles per unit volume are moving in a

conductor with speed v. In a time Dt, each particle moves vDt. If the conductor has a cross sectional area A,

then the number of particles in a given section during a given time interval is nAvDt.

Physics ch 285

Drift velocity

If each particle has a charge q, the total charge moving through the volume in a given time interval is DQ = nqvADt.

nqvAt

QI

Physics ch 286

Current density

Current per unit cross-sectional area

nqvA

IJ

Physics ch 287

Resistivity

Ratio of electric field to current density

Big resistivity means that a big E field is needed to cause a given current density,

Or that a small E field will cause a small current density

J

E

Physics ch 288

Resistivity

For metals, increases with temperature.

For semiconductors, it decreases with temperature.

For superconductors it drops suddenly as temperature decreases.

00 1 TTT

Physics ch 289

Resistance

Related to resistivity. Often more useful, because it uses total

current, not current density. It also uses potential difference instead of E field.

Measured in ohms 1 W = 1 V/A

A

lR

Physics ch 2810

Ohm’s Law

Very important

IRV

Physics ch 2811

Temperature dependence

00 1 TTRRT

Physics ch 2812

Resistors

Circuit elements designed to have a specific resistance.

Used to control current.

Physics ch 2813

Circuits

We need a complete circuit to have a steady current.

Charge moves in the direction of decreasing potential energy – like rolling downhill.

We need to have a device to move the charge back uphill – like the pump in a fountain.

Physics ch 2814

Electromotive force

What makes the charge move from lower to higher potential.

Abbreviated emf – say each letter. Batteries Solar cells Generators

Physics ch 2815

Circuits

Contain resistors, sources of emf, and possibly other circuit elements.

The algebraic sum of the potential differences around the path is zero.

In a simple loop, the current is the same everywhere.

Physics ch 2816

Sources of emf

Maintain a constant potential difference, or voltage, regardless of the current flowing through them.

Have positive and negative terminals.– The potential is higher at the positive terminal.

VE

Physics ch 2817

Internal resistance

Real sources of emf have some internal resistance to current flow.

So, IrV EIRIr E

rRI

E

Physics ch 2818

Example on page 632

Look at schematic drawings of circuits.

Physics ch 2819

Kirchoff’s loop rule

The sum of the voltages around a loop is zero.

Choose a current direction and draw it on the diagram. It’s OK if you’re wrong.– If at the end we get negative current, then the

direction was wrong. No big deal.

Physics ch 2820

Kirchoff’s loop rule

If we go across a battery from – to +, we add the voltage. + to – we subtract it.

Always subtract IR from a resistor See example on page 635

Physics ch 2821

Power

Work done per unit time, measured in watts. 1 W is 1 J/s 1 A is 1 C/s 1 V is 1 J/C (1A)(1V) = 1 J/s

IVP

Physics ch 2822

Power

Using Ohm’s law, V = IR

IRIP

RIP 2

VR

VP

R

VP

2

Physics ch 2823

Power output of emf source

rIIIVP 2 E

Physics ch 2824

Power input of emf source

rIIIVP 2 E

Physics ch 2825

Physiological effects of currents

Nervous system is electrical Currents as low as 1 mA can disrupt the

nervous system enough to cause death by fibrillation.

Larger currents through the heart may actually be safer – the heart is temporarily paralyzed and has a better chance of restarting with a normal heartbeat