Notes: Current
- If there is an electric field in a conductor, the mobile charge carriers will move.
- Ex: Electric field in metal → electrons flow.
- I = charge passing through a cross section of the conductor / time taken
- Units: C/s = A
Direction
- Current flows in the direction of electric field, or from high V to low V
- If the charge carriers have negative charge, the carriers travel in the opposite direction from the current.
- Ex: electrons in metal flow from low V to high V
Microscopic view of metal and current
- + ions locked in a regular arrangement
- - electrons move about nearly freely
- ΔV → electrons drift in uniform direction
- ALL electrons move. None accumulate or disperse.
- → current is same all along the metal
Resistance (R)
- Property of a CONDUCTING DEVICE
- ΔV = I R
- Potential difference ΔV required to cause current I is equal to I R.
- Units: Ω = Ohm = V/A = J·s/C2
Resistivity (ρ)
- Property of a CONDUCTING MATERIAL
- Units = Ω·m
- Resistance is determined by the material a device is made from, and its size/shape
- R = ρ L / A
Example: Light bulb
- A light bulb is connected to a 120V power supply.
- As a result, it carries a current of 0.20A
- What is the bulb's electrical resistance?
- The light comes from a filament: a wire that is 0.50m long, and 5×10-5m in diameter.
- What is the resistivity of the filament metal?
Resistance
- ΔV = 120V, I = 0.20A
- → R = 600Ω
- Typical Rs are 10-4 - 107 Ω
Resistivity
- L = 0.50m, A = π(2.5×10-5m)2 = 1.96×10-9m2
-
- → ρ = 2.36×10-6 Ω·m
- Typical ρs are 10-8 - 10-5 Ω·m
Problem:
- A steel block is a rectangular prism (square cross section) with dimensions 1.2mm × 1.2mm × 0.95m
- The far ends are connected to a 4.3mV power supply.
- Steel has a resistivity of 9.0×10-8 Ω·m
- How much current does the block carry?
Solution
- R = 5.9×10-2 Ω
- I = 0.072A