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Chapter 26. Current and Resistance. 26.1. What is Physics?       26.2. Electric Current       26.3. Current Density       26.4. Resistance and Resistivity       26.5. Ohm's Law       26.6. A Microscopic View of Ohm's Law       26.7. Power in Electric Circuits      

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chapter 26 current and resistance

Chapter 26. Current and Resistance

26.1. What is Physics?      

26.2. Electric Current      

26.3. Current Density      

26.4. Resistance and Resistivity      

26.5. Ohm's Law      

26.6. A Microscopic View of Ohm's Law      

26.7. Power in Electric Circuits      

26.8. Semiconductors      

26.9. Superconductors

electric current
Electric Current

The electric current is the amount of charge per unit time that passes through a plane that pass completely through the conductor.

The SI unit for current is a coulomb per second (C/s), called as an ampere (A)

direction of current
Direction of current
  • A current arrow is drawn in the direction in which positive charge carriers would move, even if the actual charge carriers are negative and move in the opposite direction.
  • The direction of conventional current is always from a point of higher potential toward a point of lower potential—that is, from the positive toward the negative terminal.
current density
Current Density
  • Current density is to study the flow of charge through a cross section of the conductor at a particular point
  • It is a vector which has the same direction as the velocity of the moving charges if they are positive and the opposite direction if they are negative.
  • The magnitude of J is equal to the current per unit area through that area element.
drift speed
Drift Speed

When a conductor does not have a current through it, its conduction electrons move randomly, with no net motion in any direction. When the conductor does have a current through it, these electrons actually still move randomly, but now they tend to drift with a drift speedvd in the direction opposite that of the applied electric field that causes the current

Here the product ne, whose SI unit is the coulomb per cubic meter (C/m3), is the carrier charge density

sample problem 26 3
Sample Problem 26-3

What is the drift speed of the conduction electrons in a copper wire with radius r=900 μm when it has a uniform current i=17 mA? Assume that each copper atom contributes one conduction electron to the current and that the current density is uniform across the wire's cross section. Mass density of copper is ρ=8.96x103 kg/m3 .

the resistance
The resistance
  • The resistance (R) is defined as the ratio of the voltage V applied across a piece of material to the current I through the material: R=V/i.
  • SI Unit of Resistance: volt/ampere (V/A)=ohm(Ω)
slide10
The resistance of a conductor depends on the manner in which the potential difference is applied to it

Ra > Rb

resistivity
Resistivity

Resistivity of a material is:

The conductivityσ   of a material is

slide12

Resistivity

  • The resistivity is an inherent property of the material
  • The resistivity of a material depends on temperature. ρ = ρ0[1 + α(T - T0)]

The term α has the unit of reciprocal temperature and is the temperature coefficient of resistivity.

slide13

 2.82

×

 3.5

×

 1.72

×

 2.44

×

 9.7

×

 95.8

×

 100

×

 1.59

×

 5.6

×

 3

×

calculating resistance from resistivity
Calculating Resistance from Resistivity
  • Resistance is a property of an object. It may vary depending on the geometry of the material.
  • Resistivity is a property of a material.
checkpoint
Checkpoint

The figure here shows three cylindrical copper conductors along with their face areas and lengths. Rank them according to the current through them, greatest first, when the same potential difference V is placed across their lengths.

sample problem
Sample Problem

A rectangular block of iron has dimensions 1.2cmx1.2cmx15cm . A potential difference is to be applied to the block between parallel sides and in such a way that those sides are equipotential surfaces (as in Fig. b). What is the resistance of the block if the two parallel sides are (1) the square ends (with dimensions ) 1.2cmx1.2cm and (2) two rectangular sides (with dimensions 1.2cmx15cm )?

sample problem 26 5
Sample Problem 26-5
  • Figure 26-11 shows a person and a cow, each a radial distance D=60m from the point where lightning of current i=10kA strikes the ground. The current spreads through the ground uniformly over a hemisphere centered on the strike point. The person's feet are separated by radial distance Δrper=0.50m; the cow's front and rear hooves are separated by radial distance Δrcow=1.50m. The resistivity of the ground is ρgr=100 Ωm . The resistance both across the person, between left and right feet, and across the cow, between front and rear hooves, is R=4.00kΩ. (a) What is the current ip through the person? (b) What is the current ic through the cow?
example
Example

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1.0 mm. Conductor B is a hollow tube of outside diameter 2.0 mm and inside diameter 1.0 mm. What is the resistance ratio RA/RB, measured between their ends?

ohm s law
Ohm's Law

Ohm's law is an assertion that the current through a device is always directly proportional to the potential difference applied to the device.

ohmic material
Ohmic Material

The ohmic material: type of materials (e.g., metals) which obeys Ohm's law.

The non-ohmic material: type of materials which does not obey Ohm's law.

  • A conducting device obeys Ohm's law when the resistance of the device is independent of the magnitude and polarity of the applied potential difference.
  • A conducting material obeys Ohm's law when the resistivity of the material is independent of the magnitude and direction of the applied electric field.
power in electric circuits
Power in Electric Circuits
  • The amount of charge dq that moves from terminals a to b in time interval dt is equal to i dt.
  • Its electric potential energy decreases in magnitude by the amount
  • The decrease in electric potential energy from a to b is accompanied by a transfer of energy to some other form. The power P associated with that transfer is the rate of transfer
  • d U/dt, which is
  • The unit of power
the transfer of electric potential energy to thermal energy
the transfer of electricpotential energy to thermal energy

The rate of electrical energy dissipation due to a resistance is

  • Caution:
  • P=iV applies to electrical energy transfers of all kinds;        
  • P=i2R and P=V2/R apply only to the transfer of electric potential energy to thermal energy in a device with resistance.
sample problem23
Sample Problem

You are given a length of uniform heating wire made of a nickel–chromium–iron alloy called Nichrome; it has a resistance R of 72 Ω. At what rate is energy dissipated in each of the following situations? (1) A potential difference of 120 V is applied across the full length of the wire. (2) The wire is cut in half, and a potential difference of 120 V is applied across the length of each half.

sample problem24
Sample Problem

A copper wire of cross-sectional area and length 4.00 m has a current of 2.00 A uniformly distributed across that area. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 30 min?

superconductors
 Superconductors

The resistivity of material absolutely disappears at very low temperatures. This phenomenon of superconductivity

conceptual questions
Conceptual Questions
  • When an incandescent light bulb is turned on, the tungsten filament becomes white hot. The temperature coefficient of resistivity for tungsten is a positive number. What happens to the power delivered to the bulb as the filament heats up? Does the power increase, remain the same, or decrease? Justify your answer.
  • Two materials have different resistivities. Two wires of the same length are made, one from each of the materials. Is it possible for each wire to have the same resistance? Explain.
  • One electrical appliance operates with a voltage of 120 V, while another operates with 240 V. Based on this information alone, is it correct to say that the second appliance uses more power than the first? Give your reasoning.
slide28
Two light bulbs are designed for use at 120 V and are rated at 75 W and 150 W. Which light bulb has the greater filament resistance? Why?
  • Often, the instructions for an electrical appliance do not state how many watts of power the appliance uses. Instead, a statement such as “10 A, 120 V” is given. Explain why this statement is equivalent to telling you the power consumption.