1. Current and Resistance
Physics 014
Current and Resistance

2. Currents and Resistors
The electric current (i) is the amount of charge moving past a point or through a region in an amount of time.

3. Currents and Resistors
The SI unit of charge is the ampere (A)
1 A = 1 coulomb per second

4. Charge is conserved
i0=i1+i2

5. Currents and Resistors
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.

6. ???
The figure shows a portion of a circuit. What are the magnitude and direction of the current i in the lower right-hand wire?
1. 4A
2. 6A
3. 8A
4. 7A

7. Currents and Resistors
The current density, , has a magnitude equal to current per unit area. SI unit of A/m2.

8. Currents and Resistors
Current i is constant. What about J?

9. Currents and Resistors
We see then that for current density

10. Currents and Resistors
We get resistance by applying a potential difference V between two points and measuring the resultant current i.
(Ohms law)

11. Currents and Resistors
The SI unit for resistance is the ohm (Ω).
1 ohm = 1 volt per ampere

12. Currents and Resistors
We can also calculate resistance from properties of materials. If we know the resistivity ρ or conductivity σ=1/ρ of a material,
length
Area

14. Currents and Resistors
Resistances connected in series can be replaced with an equivalent resistance Req that has the same current I and the same total potential difference V as the actual resistance.

15. Circuits
For n resistors in series,

16. Currents and Resistors
Can resistors in parallel be reduced to an equivalent circuit?

18. Currents and Resistors
Resistances in parallel can be replaced with an equivalent resistance Req that has the same potential difference V and same total current i as the actual resistances.

19. Currents and Resistors
For n resistors in parallel,
Proof: use the junction rule