Fall 2004 Current ECE 2317: Applied Electricity and Magnetism Prof. Valery Kalatsky Dept. of Electrical & Computer Engineering University of Houston TitleTitle

What 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 and radiators. As water is pushed through pipes by a pump, electric current is pushed through wires by a battery. A basic law of the universe is that like charges repel and unlike attract. Two negatives will repel each other. A negative and a positive will attract each other. An electron has a negative charge.

Electric CurrentElectric Current The negative (-V) terminal of a battery will push negative electrons along a wire. The positive (+V) terminal of a battery will attract negative electrons along a wire. Electric current will therefore flow from the -V terminal of a battery, through the lamp, to the positive terminal. Electric Current This is called electron current flow.

CurrentCurrent 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

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

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

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

Kinds of currentKinds of current Kinds of Current Direct Current or DC Alternating Current or AC = constant≠ constant

ExampleExample DC vs AC Thomas Alva Edison Nikola Tesla Serbian-American (7/9/1856-1/7/1943) Inventions: rotating magnetic field principle, polyphase alternating-current system, induction motor, alternating- current power transmission, Tesla coil transformer, wireless communication, radio, fluorescent lights, and more than 700 other patents. American (2/11/ /18/1931) inventor of the phonograph, the incandescent light bulb, the "kinetoscope" and many other devices that make our lives fuller and simpler. Patented 1,093 inventions. "Genius is one percent inspiration and 99 percent perspiration."

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

ExampleExample Example

ExampleExample Current Facts Smallest quantity of charge is e = 1.6 x [C]. What is smallest current?No lower limit Lightning Current Currents over 200,000 Amps have been reported. Most measurements have been in the range 5,000 to 20,000 Amps The electric chair: Dangerous for humans:0.1 Amps 5 Amps

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

Current densityCurrent density  L = distance traveled by charges in time  t. or ++++ I LL QQ Current Density

Current Crossing SurfaceCurrent Crossing Surface Current Crossing Surface

Current Crossing SurfaceCurrent Crossing Surface Integrating over the surface, Note: direction of unit normal vector determines whether current is going in or out S Current Crossing Surface

ExampleExample Example cloud of electrons N e = electrons / m 3 (a) Find: current density vector

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

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

ExampleExample Example x y 1 1 y = 1 - x

ExampleExample Quiz Lightning Current a typical lightning bolt may transfer 5 x electrons a stroke of a lightning bolt lasts less than 0.01sec A. Estimate current?More than 8,000 [A] Assuming diameter of the lightning bolt of 20cm B. Estimate current density? More than 250,000 [A/m 2 ]