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# Chapter 27 - PowerPoint PPT Presentation

Chapter 27. Current and Resistance. Intro. Up until now, our study of electricity has been focused Electrostatics (charges at equilibrium conditions). We will now look at non-equilibrium conditions, and we will define electric current as the rate of flow of charge.

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Presentation Transcript

### Chapter 27

Current and Resistance

• Up until now, our study of electricity has been focused Electrostatics (charges at equilibrium conditions).

• We will now look at non-equilibrium conditions, and we will define electric current as the rate of flow of charge.

• We will look at current at the microscopic levels and investigate factors oppose current as well.

• Current- any net flow of charge through some region.

• A similar analogy would be water current, or the volume of water flowing past a given point per unit time (shower heads, rivers etc.)

• The rate of charge passing

perpendicularly through a

given area.

• The average current

• The instantaneous current

• The SI unit of current is the Ampere (A)

• Current Direction-

• Traditional- in the direction the flow of positive charge carriers.

• Conducting Circuits- Electrons are the flowing charge, current is in the opposite direction of the flow of negative charge carriers (electrons).

• Particle Accelerator- with the beam of positive charges

• Gases and Electrolytes- the result of both positive and negative flowing charge carriers.

• At the microscopic level we can relate the current, to the motion of the charge carriers.

• The charge that passes through a given region of area A and length Δx is

• Where n is the number of charge carriers per unit volume and q is the charge carried by each.

• If the carriers move with a speed of vd, (drift velocity) such that

and

• So the passing charge is also given as

• If we divide both sides by time we get another expression for average current

• Drift Velocity-

• Charge carrier: electron

• The net velocity will be in the opposite direction of the E-field created by the battery

• We can think of the collisions as a sort of internal friction, opposing the motion of the electrons.

• The energy transferred via collision increases the Avg Kinetic Energy, and therefore temperature.

• Quick Quiz p 834

• Example 27.1

• E-Field in a conductor

= 0 when at equilibrium

≠ 0 under a potential difference

• Consider a conductor of cross-sectional area A, carrying a current I.

• We can define a new term called current density

• Units A/m2

• Because this current density arises from a potential difference across, and therefore an E-field within the conductor we often see

• Many conductors exhibit a Current density directly proportional to the E-field.

• The constant of proportionality σ, is called the “conductivity”

• This relationship is known as Ohm’s Law.

• Not all materials follow Ohm’s Law

• Ohmic- most conductors/metals

• Nonohmic- material/device does not have a linear relationship between E and J.

• From this expression we can create the more practical version of Ohm’s Law

• Consider a conductor of length l

• So the voltage equals

• The term l/σA will be defined as the resistance R, measured in ohms (1 Ω = 1 Volt/Amp)

• We will define the inverse of the conductivity (σ) as the resistivity (ρ) and is unique for each ohmic material.

• The resistance for a given

ohmic conductor can

be calculated

• Resistors are very common circuit elements used to control current levels.

• Color Code

• Quick Quizzes, p. 838-839

• Examples 27.2-27.4

• Over a limited temperature range, resistivity, and therefore resistance vary linearly with temperature.

• Where ρis the resistivity at temperature T (in oC), ρo is the resistivity at temperature To, and α is the temperature coefficient of resistivity.

• See table 27.1 pg 837

• Since Resistance is proportional to resistivity we can also use

• For most conducting metals the

resistivity varies linearly over a wide

range of temperatures.

• There is a nonlinear region as T

approaches absolute zero where

the resitivity will reach a finite

value.

• There are a few materials who have negative temperature coefficients

• Semiconductors will

decrease in resistivity

with increasing temps.

• The charge carrier

density increases with

temp.

• Quick Quiz p 843

• Example 27.6

• Superconductors- a class of metals and compounds whose resistance drops to zero below a certain temperature, Tc.

• The material often acts like a normal conductor above Tc, but falls of to zero, below Tc.

• There are basically two recognized types of superconductors

• Metals very low Tc.

• Ceramics much

higher Tc.

• Electric Current is known to continue in a superconducting loop for YEARS after the applied potential difference is removed, with no sign of decay.

• Applications: Superconducting Magnets (used in MRI)

• When a battery is used to establish a current through a circuit, there is a constant transformation of energy.

• Chemical  Kinetic  Internal (inc. temp)

• In a typical circuit, energy is transferred from a source (battery) and a device or load (resistor, light bulb, etc.)

• Follow a quanity of charge Q through the circuit below.

• As the charge moves from

a to b, the electric potential

energy increase by U = QΔV,

while the chemical potential

energy decrease by the

same amount.

• As the charge moves through the resistor, the

system loses this potential

energy due to the collisions

occuring within the

resistor. (Internal/Temp)

• We neglect the resistance

in the wires and assume that

any energy lost between bc

and da is zero.

• This energy is then lost to the surroundings.

• The rate at which the system energy is delivered is given by

• Power the rate at which the battery delivers energy to the resistor.

• Applying the practical version of Ohm’s Law (ΔV = IR) we can also describe the rate at which energy is dissipated by the resistor.

• When I is in Amps, V is in Volts, and R is in Ohms, power will be measured in Watts.

• Quick Quizzes p. 847

• Examples 27.7-27.9