ECE 1100: Introduction to Electrical and Computer Engineering Notes 12 Charge and Current Wanda Wosik Associate Professor, ECE Dept. Spring 2011 Slides adapted from Dr. Jackson 1

Charge proton: + charge electron: - charge 1 Coulomb [ C ] =  protons 1 proton: q = 1 /  [ C ] =  [ C ] 1 electron: q =  [ C ] Atomic number of atom = # protons or electrons / atom 2

Example How many Cu atoms have -1 [ C ] of electrons? Atomic number = 29 1 atom: q e = 29 (  ) [ C ] so or 3

1 C of Charge vs. 2 C of Charge. Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 4

An Element Compound Is Made Up of Many Atoms Is Made Up of Many Molecules. Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 5

Positive and Negative Charges. Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 6 FIGURE 1-9 Electron Migration Due to Forces of Positive Attraction and Negative Repulsion on Electrons.

Current Current 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.) Units: One Ampere [ A ] = 1 Coulomb/second [ A ] 1 [ C/s ] [ A ] 1 [ C/s ] Note: the red arrow indicates the direction of movement. 8

Current (cont.) 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 [A] flow rate = 1 [C/s] Ions do not move 9

Current (cont.) 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. 10

Voltage Potential energy describes the capacity to do work ex. E=mgh (gravitation) will change to kinetic energy E=mv 2 /2. 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 [V] Work is done equal to  |U| Voltage related to energy loss/gain Ex. q=1C, V AB =1V Energy gain/loss 1Joule 11

Current (cont.) 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 V 9  1 [A] V 9  1 [A]

Current (cont.) 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 [A] flow rate = 1 [C/s] -1 [A] 13

Current (cont.) We can say that we have 1 Amp flowing down through the resistor, or –1 Amp flowing up through the resistor V 9  1 [A]-1 [A] or 14

Example 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.) - - I = +1 [A] I = ? - - I = -1 [A] I = ? 16

Reference 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

Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 18 Physical Appearance. Schematic Symbol. The Battery A Source of Voltage.

Component and Schematic Symbol Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 19 Components. Example Circuit.

Using the Voltmeter to Measure Voltage. Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 20

Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 21 Lamp 1 Lamp 2. Measuring the Voltage Drop Across Components

Power Supply Unit. Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 22

Closed Switch Causing a Closed Circuit Nigel P. Cook Electronics: A Complete Course, 2e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. 23. (a) Pictorial. (b) Schematic.

Reference Direction (cont.) Example: Digital multimeter (DMM) The reference direction is pointing in to the red connector and out of the black connector mA redblack I 24

Reference Direction (cont.) Example: Using the DMM in a simple circuit V 9  1 [A] A red black V 9  IxIx Measuring I x with DMM 25

Reference Direction (cont.) 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 R 26

Mathematical 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 Allowing for a non-steady current: q reference direction arrow 27

Definition 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 - + All electrons flow -  + (it is a conductor) dN – total # of charges passing area A v - drift velocity carrier density n – varies with materials A

Definition 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

Example 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 + + I _ _ 30

Example (cont.) I + + I - - Note: the formula always gives the correct sign, which agrees with Ben Franklin’s convention! 31 in 1 s

Example i ( t ) Given: q ( t ) is the charge that crosses the dashed line going from left to right, in the time interval ( 0, t ). Find i ( t ) 32

Example Find q p ( t ) = charge that leaves the positive terminal of the battery in the time interval ( 0, t ). + - v ( t ) i ( t ) Given: q (t) = charge that crosses dashed line going from left to right between ( 0, t ) [ s ]. + - v ( t ) i ( t ) q (t) 33

Example (cont.) Hence So Integrating, we have Hence 34 q t Ex. charging a capacitor

Example Find q n (t) = charge that leaves the negative terminal of the battery in the time interval ( 0, t ). Given: + - v ( t ) i ( t ) + - v ( t ) i '(t)i '(t) q (t)q (t) 35

Example (cont.) + - v ( t ) 36