Electrical Current And Resistance Physics

Current, Resistance and Electromotive Force Young and Freedman Chapter 25

Electric Current: Analogy, water flowing in a pipe H20 gallons/minute

Individual molecules are bouncing around with speeds of km/s!

“Flow Rate” is the NET amount of water passing through a surface per unit time

Net water velocity is m/s

I Coulombs/s

“Electric Current” is the NET amount of charge passing through a surface per unit time

- - - - - -

Individual electrons are bouncing around with very high speed Electron “drift velocity may be mm/s

Electric Current In a Conductor, Charges are free to move. The charges may be positive; This is usually relevant only for “special cases” like ions in a solution. (Holes in semiconductors act like positive charges)

The charges may be negative; This is the normal case for metallic conductors.

dQ I= dt

Inside a conductor there are LOTS of charges There could be 1024 electrons /cm2+ Area A

Current I

vd is “drift velocity”

r vd n = # of charges q per m3 Total Current through area A is given by

I = nqvd A Current per unit area is given by

I J = = nqvd A J can vary in magnitude and direction in Space

r r J = nqvd

Vector Current Density

Conductors, in general, follow Ohm’s law For many materials, the local current density is proportional to the local electric field

v r E J= !

E or != J ρ is known as the Resistivity of a material A material with a linear relationship between J and E is said to follow “Ohm’s Law” Important note: Not all material follow Ohm’s Law. Most metals do follow Ohm’s Law so when we speak of a metallic conductor we are implicitly assume that the material follows Ohm’s Law. This is not to be confused with a “perfect” conductor which has zero resistivity. There are real materials called “superconductors” There are many important examples of “Non-Ohmic” materials. Many extremely important semi-conductor devices are non-ohmic.

Current V E= L

r v E = !J Ohm’s Law

Uniform E Field

What is the total Current through this object? I = JA E I= A ! V I= A L! L! V= I A

Collect all the terms that describe the object and call them “R” the:

RESISTANCE

V = IR Usual Statement of Ohm’s Law

Resistivity and Resistance IMPORTANT: Do not confuse “Resistivity” with Resisitance Resistivity is a property of a type of Material (copper, steel, water,…) Resistance is a property of a particular, specific object (a car key, a piece of wire…)

Circuits Direct Current – “DC” • In a DC Circuit ALL quantities (Voltage, Current, …) are constant • Consider that the circuit has been running for a long time and will continue to run longer. In a steady state system – Charge can only flow in a “Loop” E I

-

+ + +

E=0 I=0

V Current can flow in continuous loop BUT If Resistance is NOT ZERO, We require something to keep current flowing, “ELECTRO MOTIVE FORCE”

ε

Continuing with “flowing water” analogy: EMF In a closed water “circuit” because of viscosity (“fluid friction”), there must be some “motive force” to maintain a steady state flow of water. In a closed electrical “circuit” because of resistivity (“electrical friction”), there must be some “electro-motive force” to maintain a steady state current.

ε

An Ideal “Electromotive Force” ε provides a constant voltage between two “terminals” – No Matter How Much Current Flows!

Inside the “Ideal EMF” r A Non Electrostatic Force Fn acts on the the charges inside the EMF. This cause the chargesrto be displaces and leads to a electrostatic force Fe which “balances” the non-electrostatic force.

A “resistive” path

Potential difference between ends of resistive path:

V =!

V = IR }

! = IR

Symbols for circuit elements Ideal conductor - generally assume that that R=0 Ideal EMF

NOTE – device is asymmetric

Ideal Resistor

EMF with internal resistance

Ideal Voltmeter - generally assume that that R=∞ - No current flows through an ideal voltmeter A

Ideal Ammeter - generally assume that that R=0 Electrically, an ideal ammeter is a perfect conductor

Open Circuit EMF Ex 25.2 Question: What do the meters read?

First simplify circuit by replacing the meters by equivalent resistors: No complete circuit means No current c

Vab = Vac + Vcb Vab = IR + Vcb Vab = 0 + Vcb Vab = ! = 12V Voltmeter reads V=12 volt Ammeter reads A= 0 amperes

Open Circuit EMF Ex 25.2

=

c

Electrically

First Determine the Current:

V = IRtotal V = I (r + R) I 12V I= = = 2A ( r + R ) 6!

Next Determine the Voltage:

Vab = Vcb " Vac Vab = # " Ir Vab = 12v " ( 2 A)( 2!) Vab = 8V

Important Suggestion for doing problems: First completely solve the problem algebraically… Then substitute numerical quantities to determine the numerical answer

Electric potential through a complete circuit

FIGURE 25.20

If I go around the circuit and come back to the same point, THE VOLTAGE MUST BE THE SAME!

Power in electric circuits Power is defined as Energy (Work) per Unit Time

dW = VabdQ dW dQ = Vab dt dt dW = Vab I dt For Pure Resistance

dW P= = IV dt V2 2 P=I R= R

but V = IR

The sign of the power is important

dW > 0

Power added to system

Changes chemical energy to electrical energy and adds it to the energy in the circuit

dW < 0

Power removed from system Changes electrical energy to heat and removes it from the circuit

Chapter 25 Summary

Chapter 25 Summary cont.

End of Chapter 25 You are responsible for the material covered in T&F Sections 25.1-25.5 You are expected to: •

Understand the following terms: Current, Resistivity, Resistance, EMF, Internal Resistance, Open Circuit, Complete Circuit, Ammeter, Voltmeter, Short Circuit, Power

•

Determine Current and Voltage in a simple circuit.

•

Understand how voltmeters and ammeter’s are used and how they respond.

•

Determine power dissipation in a simple circuit

Recommended Y&F Exercises chapter 25: 1, 10, 11, 31, 32, 35, 36, 44, 49