Chapter 18 Electric Currents

Objectives: The students will be able to: Describe what resistivity depends on. Solve problems relating to resistivity.

Electrical Resistance When electric current flows through a metal wire there exists a hindrance to the flow, known as electrical resistance. This is because as the electrons move through they will collide with the atoms of the conductor. The SI unit of resistance is the ohm (Ω), after Georg Simon Ohm ( ), a German physicist, who discovered Ohm ’ s law. A resistor is a material that provides a specified resistance in an electric circuit.

18.4 Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: (18-3) The constant ρ, the resistivity, is characteristic of the material.

Resistance,R and Resistivity,ρ The resistance of a conductor is directly proportional to the length since the current needs to pass through all the atoms in the length. The resistance is inversely proportional to the cross-sectional area since there is more room for the current to pass through. The above observations can be combined and the resistance, R of the conductor is written as follows,

Resistance Depends on type of material, size and shape, temperature. R=ρ L A L: length of the wire A: cross-sectional area ρ: resistivity (inherent to material)

18.4 Resistivity

Example: What happens to the resistance when the length is doubled and the area is quadrupled? Answer: It changes by 1/2

Factors Affecting Resistance 1. The length L of the material. Longer materials have greater resistance. 1 1 L 2 2 2L 2. The cross-sectional area A of the material. Larger areas offer LESS resistance. 2 2 A 1 1 2A

Factors Affecting R (Cont.) 3. The temperature T of the material. The higher temperatures usually result in higher resistances. 4. The kind of material. Iron has more electrical resistance than a geometrically similar copper conductor. RoRoRoRo R > R o R i > R c CopperIron

Example What length L of copper wire is required to produce a 4 m  resistor? Assume the diameter of the wire is 1 mm and that the resistivity  of copper is 1.72 x . m.

Example What length L of copper wire is required to produce a 4 m  resistor? Assume the diameter of the wire is 1 mm and that the resistivity  of copper is 1.72 x . m. A = 7.85 x m 2 L = m Required length is: Period 1 stopped here.

18.4 Resistivity For any given material, the resistivity increases with temperature: (18-4) Semiconductors are complex materials, and may have resistivities that decrease with temperature. Multiply the above equation by L/A; so using Equation 18-3 you can get the next equation on next slide. Temperature coefficient is α

Solve this equation to get….

Temperature Coefficient For most materials, the resistance R changes in proportion to the initial resistance and to the change in temperature  t. For most materials, the resistance R changes in proportion to the initial resistance R o and to the change in temperature  t. Change in resistance: The temperature coefficient of resistance,  is the change in resistance per unit resistance per unit degree change of temperature.

Example The resistance of a copper wire is 4.00 m  at 20 0 C. What will be its resistance if heated to 80 0 C? Assume that  = /C o.

R o = 4.00 m  t = 80 o C – 20 o C = 60 C o  R = 1.03 m  R = R o +  R R = 4.00 mm R = 4.00 m  m  R = 5.03 m 

Homework Chapter 18 Problems #12, 13, 21 Note: for Cu use 3 x 10 -5

Closure: Kahoot 18-4