Fall 2004

Current

ECE 2317: Applied Electricity and Magnetism

Prof. Valery KalatskyDept. of Electrical & Computer Engineering

University of Houston

Title

What 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 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.

Current

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 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 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.

Qi

t

reference direction arrow

i

Q

dQi t

dtmore generally,

Mathematical Definition of Current

Kinds of current

Kinds of Current

Direct Current or DC

Alternating Current or AC

Qi

t

= constant

dQi t

dt ≠ constant

Example 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 (2/11/1847-10/18/1931)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."

Example Example

i(t)Q

dQi t

dt

10 2 cos 2 60 [A]i t t

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

1

2

0

0

( )

( )

( ) 0 0

t

t

Q t i t dt C

i t dt C

i t dt Q

Alternating Current (AC)

Example

0

0

0

( )

10 2 cos 2 60

110 2 sin 2 60

2 60

t

t

t

Q t i t dt

t dt

t

2sin 2 60 [C]

12Q t t

Example

Example Current Facts

Smallest quantity of charge is e = 1.6 x 10-19[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 density

Current Density

2[A/m ]I

JS

2ˆ [A/m ]I

S

J

+ + + +S I

The current density vector points in the direction of current flow (positive charge motion)

v

Current density

// Q t LI Q t Q LJ

S S S L V t

L = distance traveled by charges in time t.

vJ vor ˆvvJ

vJ vor

+ + + +S I

L

Q v

Current Density

Current Crossing Surface

Current Crossing Surface

ˆˆ n tJ J J n t n

S

ˆnJn

ˆtJt

ˆnI J S S J n

n

S

J

Current Crossing Surface ˆI S J n

Integrating over the surface,

ˆS

I dS J nNote: direction of unit normal vector determines whether current is going in or out

nJ

S

Current Crossing Surface

Example Example

- - - - --- - - - --

cloud of electrons

Ne = 1020 electrons / m3

ˆ2.5 [m/s]v z

(a) Find: current density vector

vJ v

20 3 1910 [1/ m ] 1.602 10 [ ]v e eN q C

2ˆ40.05 [A/m ] J z

Example Example

(b) Find: current in wire with reference direction shown

In

ˆ

ˆ ˆ40.05

40.05

40.05

S

S

S

I dS

dS

dS

A

J n

z z

2

2

40.05

40.05 0.001

I a

41.2582 10 [A]I

Iz

radius a = 1 [mm]

- - - - --

Example Example

ˆ ˆ 3S S S

I dS dS xy dS J n J z

2 3 2 2ˆ ˆ ˆ3 3 3 [A/m ]x y z y xy J x y z

x

y

z

(1,0,0)(0,1,0)

S

Find: current I crossing surface in the upward direction

Example Example

( )1

0 0

12

00

12

0

14 3 2

0

3

3

3

2

31

2

3 1 2 1

2 4 3 2

S

y x

y x

I xy dS

xy dy dx

xy dx

x x dx

x x x

x

y

0.125 [A]I

1

1y = 1 - x

Example Quiz

Lightning Current

a typical lightning bolt may transfer 5 x 1020 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/m2]