Ohm’s Law

Physics 102Professor Lee

CarknerLecture 14

PAL #13 Capacitors

What is the charge stored on the capacitor?

Jury-rig a replacement out of metal foil and

Teflon coating (k = 2.1, thickness = 0.01 mm). C = 0A/d A = Cd/0 = (5X10-6)(0.00001)/(2.1)(8.85X10-12)

How can such a device be portable?

Circuit Theory There are three key variables used in

circuit theory:

V provides energy and causes charges to move

Energy can be extracted from the current due to resistance (symbol: R)

Current The current is the flow rate of charge

and is defined as:

The units are amperes (amps) or coulombs per second

The most common charge carrier is the electron

Inside a Wire

What goes on inside a current carrying wire? An applied potential difference makes them

want to move in a certain direction (against the field)

They undergo many collisions and move in a random walk

Drift Speed

We can find the drift speed in terms of

the properties of the wire:

Where I is the current, n is the electron density, q is the charge on the electron and A is the cross sectional area of the wire

Electron Motion

Current Conundrums The drift speed is very small (~mm per second),

yet the effect of current is felt instantaneously

Electrons move randomly, yet current flows in only one direction

The direction of the current is opposite the motion of the electrons

emf

A battery maintains a potential difference across its terminals which can do work by moving charge

The amount of work done by a battery is just the amount of charge moved times the emf

W = Q

Resistivity

Why? The materials resist the flow of current Good conductors have low resistivity,

good insulators have high resitivities

Resistance The total resistance of the material also

depends on its size

The resistance can be written as:R = (L/A)

The units of resistance are ohms (volts per ampere)

Ohm’s Law

How much current do you get if you put a potential difference V across a wire with resistance R?

I = V/R

This relationship is called Ohm’s Law

V = IR Ohm’s law is very important, memorize it!

However, the law only holds for certain types of materials (called ohmic)

Simple Circuit

Using Ohm’s Law

Ohm’s law quantifies the way circuits work

Can write in different ways: V = IR

I = V/R

Today’s PAL

A 1.5 volt battery produces 167 A of current when connected to a 1 meter long, 2 mm thick wire. What is the wire made of?

Discuss the validity of the following claim: “The relationship R = V/I tells us that

the resistance of a wire is directly proportional to the potential difference applied to it.”

Temperature and Resistance

Electronic devices get hot! Temperature also affects electronic

properties

This increased random motion means collisions are more frequent and it is harder for current to flow

Superconductivity

If we set up a current in a wire and then take away the battery the current fades to zero

If the resistance was zero the current would keep flowing even without a battery

Such materials are called superconductors Resistance generally decreases with

decreasing T

Energy in Electric Circuits

As the charges flow (as current) they convert the potential energy to kinetic energy

We should be able to relate the potential difference, current and resistance to the energy produced

Energy Dispersion Rate Each charge that passes through the battery

gains energy that it will later lose as heat

Each charge then gives up its energy so the total power (energy per second) depends on the rate of charge flow or current

V = P

Power Using Ohm’s law (V = IR) we can write:

P = I2R and P = (V)2/R

Current and power can then be computed

Lightbulbs A common circuit element is the lightbulb

Household lightbulbs are rated in watts

In the US, most power outlets produce 120 volts of potential difference Those that do not use a transformer

Joule Heating The conversion of electrical energy into

heat is called joule heating

Joule heating is seen in the natural world: Can produce energy in the Earth’s atmosphere

Next Time

Read 21.4-21.5 Homework Ch 21, P: 24, 26, 42 Final:

Section 1: Tuesday, Feb 25, 9-11 am Section 2: Thursday, Feb 27, Noon-

2pm