Ohm’s Law Physics 102 Professor Lee Carkner Lecture 14

PAL #13 Capacitors   What is capacitance?  Q= CV  C = Q/V = 0.005/1000 =  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 )  A =  How can such a device be portable? 

Circuit Theory   We have already discussed potential difference   This charge motion is called the current (symbol: I)  Energy can be extracted from the current due to resistance (symbol: R)

Current  I =  Q/  t  The units are amperes (amps) or coulombs per second   The most common charge carrier is the electron

Inside a Wire   The wire is full of electrons   However, the electrons do not move in a straight line   Electrons do not move freely, directly or rapidly

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 

Resistivity   Why?  The materials resist the flow of current   Good conductors have low resistivity, good insulators have high resitivities  Resistivity is a property of a particular type of material rather than of a particular wire

Resistance   Short, wide wires have less resistance than long, narrow wires  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?  High voltage, low resistance means large current   Commonly written as: V = IR   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:   The voltage varies directly with resistance when current is constant   High voltage and low resistance means high current

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  Resistors convert energy from the current into heat   Temperature also affects electronic properties   This increased random motion means collisions are more frequent and it is harder for current to flow  Resistance generally increases with temperature

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   Superconductors have R go to zero as T gets small

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   The energy per electron is  PE = q  V so energy per coulomb is  V   (Energy/Coulomb)(Coulomb/Second) = (Energy/Second)  V = P

Power  Using Ohm’s law (  V = IR) we can write:  In general we will know the values of R (since it depends on the properties of the resistor) and  V (since we should know the voltage of our source or battery) 

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

Coronal Loop on the Sun

Joule Heating   This is how an electrical resistance heater works  Joule heating is seen in the natural world:   Can produce energy in the Earth’s atmosphere 

Next Time  Read: , 18.6, 19.7  Homework: Ch 18, P 35, (+one not in book), Ch 19, P 5, 9