1. Prof. Jeffery T. Williams Dept. of Electrical & Computer Engineering University of Houston Fall 2004 Current ECE 2317: Applied Electricity and Magnetism

2. What is electric currentWhat is electric currentWhat is electric currentWhat is electric current What is Electric Current? Electric current is a flow of charged particles (usually electrons) through conductors (usually wires and electronic components). It can be likened to the flow of water through pipes. Just as water is pushed through pipes by a pump, electric current is pushed through wires by a battery or voltage source. Electrons will flow from the negative terminal of a battery, through the lamp, to the positive terminal. Direction of electron flow Electric current

3. Current is the flow of charge. The unit for current is the Ampere [Amp, A]. Current 1 Amp = 1 [C/s] Convention (Ben Franklin) : positive current is in the direction of positive charge flow. ++++ current flows from left to right. velocity

4. Sign convention #1: a positive current flowing one way is equivalent to a negative current flowing the other way. Reference Direction ++++ 1 [ A ] flow rate is 1 C per second velocity - 1 [ A ] or Note: the arrow is called the reference direction arrow.

5. Sign convention #2: positive charges moving one way is equivalent to negative charges moving the other way. Reference Direction 1 [ A ] ---- flow rate is 1 C per second velocity - 1 [ A ] equivalent to: ++++ flow rate is 1 C per second velocity or

6. Mathematical definition of current Definition of Current reference direction arrow  Q = amount of charge (positive or negative) that crosses the reference plane in the direction of the reference arrow in time  t. i QQ more generally,

7. Types of Current

8. Example i(t) QQ Find: charge Q that crosses dashed line going from left to right in the time interval (0, t ) [S].

9. Example (cont.)

10. Current Density ++++ I The current density vector points in the direction of current flow (positive charge motion)

11. Current Density Vector (cont.)  L = distance traveled by charges in time  t. or ++++ I LL QQ

12. Current Crossing Surface

13. Integrating over the surface, Note: direction of unit normal vector determines whether current is going in or out S

14. Example --- -- - --- -- - cloud of electrons N e = 10 20 electrons / m 3 (a) Find: current density vector

15. Example (b) Find: current in wire with reference direction shown I I radius a = 1 [mm] --- -- -

16. Example x y z (1,0,0) (0,1,0) S Find: current I crossing surface in the upward direction

17. Example x y 1 1 y = 1 - x