ECE 1100: Introduction to Electrical and Computer Engineering Notes 12 Charge and Current Wanda...

ECE 1100: Introduction toECE 1100: Introduction toElectrical and Computer EngineeringElectrical and Computer Engineering

Notes 12Charge and Current

Wanda WosikAssociate Professor, ECE Dept.

Spring 2011

Slides adapted from Dr. Jackson1

ChargeCharge

proton: + charge

electron: - charge

1 Coulomb [C] = 6.2414 1018 protons

1 proton: q = 1 / 6.2414 1018 [C] = 1.6022 10 -19 [C]

1 electron: q = -1.6022 10 -19 [C]

Atomic number of atom = # protons or electrons / atom2

ExampleExample

How many Cu atoms have -1 [How many Cu atoms have -1 [CC] of electrons?] of electrons?

Atomic number = 29

1 atom: qe = 29 (-1.6022 10-19 ) [C]

19

1[C]atoms

29 1 6022 10 [C/atom]#

.

so

17# atoms 2 1522 10. or

3

1 C of Charge vs. 2 C of Charge.1 C of Charge vs. 2 C of Charge.

Nigel P. CookElectronics: A Complete Course, 2e

Copyright ©2004 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.4

An Element An Element CompoundCompoundIs Made Up of Many Atoms Is Made Up of Many Atoms Is Made Up of Many Molecules.Is Made Up of Many Molecules.




Positive and Negative Charges.Positive and Negative Charges.




FIGURE 1-9 FIGURE 1-9 Electron Migration Due to Electron Migration Due to Forces of Positive Attraction and Negative Forces of Positive Attraction and Negative Repulsion on Electrons.Repulsion on Electrons.

CurrentCurrentCurrent is the rate of flow of charge

water analogy:

pipe with water

wire with current

+ + + + current flows from left to right

Convention: current flows in the direction of positive charge motion (established by Benjamin Franklin).

7

Current (cont.)Current (cont.)

Units: One Ampere [A] = 1 Coulomb/second

+ + + +

1 [A]1 [C/s]

+ + + +

1 [A] 1 [C/s]

Note: the red arrow indicates the direction of movement. 8


In reality, the electrons are the charges that move in a wire.

Convention: electrons moving in one direction is equivalent to positive charges moving in the other direction.

- - - -

1 [A] flow rate = 1 [C/s]

Ions do not move

9


In fact + charges can also flow ≈ current flows

In semiconductors, both electrons (-) and holes (+) are the charges that move: diodes, transistors, resistors.

In electrochemistry + ions flow ionic current: metal electroplating, fluidics, plasma etc.

10www.saskschools.ca/curr_content/chem30_05/6_redox/redox2_2.htm

VoltageVoltage

Potential energy describes the capacity to do work ex. E=mgh (gravitation) will change to kinetic energy E=mv2/2.

€

U =kQq

r[eV ]

q

Electric potential energy U: refers to a charge q moved in an electric field E generated by another charge Q. Charge will experience force F

€

E =F

q=

kQq

qr2 =kQ

r2 [V /m]

€

€

F =kQq

r2

= qE

[V]

Work is done equal to |U|

€

V[V ] =U[eV ]

q[e]

Voltage related to energy loss/gain

Ex. q=1C, VAB=1VEnergy gain/loss 1Joule 11

http://hyperphysics.phy-astr.gsu.edu/


We can visualize positive charges coming out of the positive terminal of a battery.

In reality, it is the negative charges that come out of the negative terminal of the battery.

+

-9 V 9 1 [A]

++++

+

-9 V 9 1 [A]

- - - -

12


It is convenient to introduce the concept of negative current. That is, current is allowed to be either positive or negative.

Convention: a positive current flowing in one direction is equivalent to a negative current flowing in the opposite direction.

- - - -

1 [A]flow rate = 1 [C/s]

-1 [A]

13


We can say that we have 1 Amp flowing down through the resistor, or –1 Amp flowing up through the resistor.

+

-9 V 9 1 [A] -1 [A]or

14

ExampleExample

The flow rate of charge is 1[C/s] in each case. (The red arrow denotes the direction of the velocity.)

+ + + + I = +1 [A]

I = ?

+ + + + I = -1 [A]

I = ?

Determine the current in the direction shown.

15

Example (cont.)Example (cont.)

- - - - I = +1 [A]

I = ?

- - - - I = -1 [A]

I = ?

16

Reference DirectionReference Direction

A reference direction arrow is a label that tells us the direction of current that we are calculating.

A reference direction arrow does not tell us which way the current is actually flowing (since the value of the current may be either positive or negative).

Note: If I > 0, current is flowing to the right. If I < 0, current is flowing to the left.

I

17




Physical Appearance. Schematic Symbol.

The BatteryA Source of Voltage.

Component and Schematic Symbol




Components. Example Circuit.

Using the Voltmeter to Measure Voltage.



All rights reserved.

20




21

Lamp 1 Lamp 2.

Measuring the Voltage Drop Across Components

Power Supply Unit.




Closed Switch Causing a Closed CircuitClosed Switch Causing a Closed Circuit




23

. (a) Pictorial. (b) Schematic.

Reference Direction (cont.)Reference Direction (cont.)

Example: Digital multimeter (DMM)

The reference direction is pointing in to the red connector and out of the black connector.

1.23 mA

red black

I

24


Example: Using the DMM in a simple circuit

+

-9 V 9 1 [A]

-1.00 A

red black

+

-9 V

9

Ix

Measuring Ix with DMM

25


Reference directions are very useful in circuit analysis, because we often do not know ahead of time which way the current is actually flowing.

Note: If I > 0, the actual current is flowing to the right. If I < 0, the actual current is flowing to the left.

I

complicated circuit

complicated circuit

R

26

Mathematical Definition of CurrentMathematical Definition of Current

q = amount of charge (could be positive or negative) that passes through the plane in the direction of the reference direction arrow in a

time t.

Let:I

observation plane

qI

t

Allowing for a non-steady current: dqi t

dt

q

reference direction arrow

27

Definition of CurrentDefinition of Current

28

Current I is a flow of charge. • If the flow is constant, charge does not change q/t, and it last some time t we can find relation

• In the case of “alternating current” ac, there is instantaneous charge change and we have

€

i[A] =dq[C]

dt[s]€

q[C] = I[A]t[s]

- +

All electrons flow -+ (it is a conductor)

dN – total # of charges passing area A

v - drift velocity

carrier density n – varies with materials

€

qdN = q(vdt • A)n

€

I =d(qN)

dt= nq • v • A

€

q(dN) = dq • N + q • dN

A

Definition of CurrentDefinition of Current

I is used for a steady-state current (not changing with time).

Note on notation (ECE 2300 notation):

i (t) is used for a time-varying current (changing with time).

29

ExampleExample

The flow rate is 1 [C/s]. For each part, determine the charge q to be

used in the current formula, assuming t = 1 [s]. Then find the current I

I+ + + +

1[C]q 1[A]I

I_ _ _ _

1[C]q 1[A]I

qI

t

30


1[A]I

I+ + + +

1[C]q

I- - - -

1[C]q 1[A]I

Note: the formula always gives the correct sign, which agrees with Ben Franklin’s convention! 31

in 1 s

in 1 s

ExampleExample

i (t)

Given: q (t) is the charge that crosses the dashed line going from left

to right, in the time interval (0, t).

1 [C]tq t e

Find i (t)

[A]t tdqi t e e

dt

32

ExampleExample

Find qp (t) = charge that leaves the positive terminal of the

battery in the time interval (0, t).

+

-v (t) i (t)

Given: [A], 0ti t e t

q (t) = charge that crosses dashed line going from left to right between (0, t) [s].

dqi t

dt

+

-v (t) i (t)

q (t)

33


pdqi t

dtHence pq t q t So

Integrating, we have 0 0

t tpdq

i t dt dtdt

Hence 0

0t

p pi t dt q t q

34

0

0

1t

tt t tpq t e dt e e

1 [C]tpq t e q

t

Ex. charging a capacitor

ExampleExample

Find qn (t) = charge that leaves the negative terminal of the battery in

the time interval (0, t).

Given: [A], 0ti t e t

[A], 0ti' t i t e t

dqi' t

dt

+

-v (t) i (t)

+

-v (t)

i '(t)

q (t)

nq t q t35


1 [C]tnq t e

+

-v (t) ndq

i' tdt

0

0 0

1t t

tt t tnq t i t dt e dt e e

i' t

36

ECE 1100: Introduction to Electrical and Computer Engineering Notes 12 Charge and Current Wanda...

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