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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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Chapter 27

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.

27 1 electric current
27.1 Electric Current

  • 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


  • 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

27 2 resistance
27.2 Resistance

  • 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

27 4 resistance and temperature
27.4 Resistance and Temperature

  • 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



  • There are a few materials who have negative temperature coefficients

  • Semiconductors will

    decrease in resistivity

    with increasing temps.

  • The charge carrier

    density increases with



  • Quick Quiz p 843

  • Example 27.6

27 5 superconductors
27.5 Superconductors

  • 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)

27 6 electrical power
27.6 Electrical Power

  • 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