Ohm’s Law Physics 102 Professor Lee Carkner Lecture 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 =  0 A/d  A = Cd/  0 = (5X10 -6 )( )/(2.1)(8.85X )   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 E  

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 = I 2 R 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  Homework Ch 21, P: 24, 26, 42  Final:  Section 1: Tuesday, Feb 25, 9-11 am  Section 2: Thursday, Feb 27, Noon-2pm