1. Resistance
and resistivity

2. Current Current is sort of a vector
Direction is constrained by conductor
Restricted to forward or backward (+ or –)

3. Resistance Current does not flow unhindered
Electrical resistance is analogous to friction or drag
Expressed as potential needed to maintain a current

4. Ohm’s Law DV DV = voltage = electric potential drop I = R I = current
R = resistance
Good conductors have low resistance.
Unit of resistance : V / A = ohm (W) 4

5. Voltage Causes Current
Potential drop is the cause.
Current is the effect.
Resistance reduces the effect of potential.

6. Does it Work?
Approximation of varying utility: R is independent of DV and I
When true, the material is ohmic

7. Poll Question
If you want to increase the current through a resistor, you need to
Increase the resistance or voltage.
Decrease the resistance or voltage.
Increase the resistance or decrease the voltage.
Decrease the resistance or increase the voltage.

8. Ohm’s Law Rearranged If you know two, you can find the third. DV DV
DV = IR
R = R I
Good conductors have low resistance.
I = current
DV = potential
R = resistance

9. Example
A 1.5-V battery powers a light bulb with a resistance of 9 W. What is the current through the bulb?
Ohm’s Law I = V / R
V = 1.5 V; R = 9 W
I = (1.5 V ) / (9 V/A) = 1/6 A

10. Resistivity For current through a cylinder: Longer L  greater R.
Greater A  smaller R.
More resistive material  bigger R.

11. Resistivity R = r L/A r is Resistivity Unit: ohm·meter = Wm
More or less constant depending on material, conditions

12. Resistivity Intensive quantity
Does not depend on the amount of material, only its conditions
Predictive value when mostly constant (ohmic)

13. Resistivities vary widely
Silver
1.59  10–8 Wm
Graphite
3.5  105 Wm
Quartz
75  1016 Wm

14. Example
The resistivity of copper is 1.710–8 Wm. What is the resistance of a 100-km length of copper wire that is 1/4” in diameter?

15. Classes of Conductors How resistivity changes with temperature
a = temperature coefficient of resistivity

16. Classes of Conductors
How resistivity changes with temperature

17. dissipated by a resistor
Power
dissipated by a resistor

18. Electric Power Power = VI Potential is energy per charge: V = DE / q
Current is charge per time: I = q /Dt
So, (potential times current) = (energy per time) = power
Good conductors have low resistance.
Power = VI

19. Group Work Power P = VI and V = IR. Using these, show that: P = I2R
P = V2/R