# E40M Charge, Current, Voltage and Electrical Circuits KCL, KVL, Power & Energy Flow. M. Horowitz, J. Plummer, R. Howe 1

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1 E40M Charge, Current, Voltage and Electrical Circuits KCL, KVL, Power & Energy Flow M. Horowitz, J. Plummer, R. Howe 1

2 Reading For Topics In These Slides Chapter 1 in the course reader OR A&L Two terminal elements Voltage source; resistor; wires A&L Circuit Laws KCL & KVL M. Horowitz, J. Plummer, R. Howe 2

3 Understanding the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage and power behave in circuits 2. Electrical devices constrain current and voltage 3. Diodes including solar cells work 4. Voltage converter works (later in the quarter). M. Horowitz, J. Plummer, R. Howe 3

4 What Does It Do? Takes energy from sun light Stores it Provides that energy later To charge your cellphone Create reading light, flashlight How does it do that? M. Horowitz, J. Plummer, R. Howe 4

5 How Our Solar Charger Works Converts some energy from sunlight into an electrical signal That electrical signal connects to a rechargeable battery So energy flows from solar cell to battery Another electrical signal connects the battery to the USB port So energy can flow to the USB, and charge your phone So we need to understand electrical signals M. Horowitz, J. Plummer, R. Howe 5

6 Fluidic Circuits Electrical Circuits Flow Current: i Reservoir Pump Generator 5 V Voltage Source Device Pond M. Horowitz, J. Plummer, R. Howe 6

7 Electrical Charge Current: i In electrical systems current is carried by charges, usually electrons 5 V Voltage Source wire Device Charge is measured in Coulombs 1 coulomb is a lot of charge Each electron has a charge of -1.6 x Coulombs Charge can flow (move) in a material that conducts wires, devices (power is dissipated if they have resistance) Like magnets, opposite charges attract; like charges repel. M. Horowitz, J. Plummer, R. Howe 7

8 Electrical Current Current: i Moving charge is called current Current is the flow of charge per second Past some measured point 5 V Voltage Source Device Its unit is the Ampere, usually called amps and abbreviated A 1 A = 1 Coulomb/sec = 1 Cs -1 The symbol for current is usually i M. Horowitz, J. Plummer, R. Howe 8

9 Electrical Current is Continuous i = 1 A i =? The current flow in a wire remains the same along it, since there are no leaks of charge out of the wire 5 V Voltage Source Device The current flows in one terminal of the device and out the other i =? i =? The wires and the device are neutral (zero charge), even though current is flowing through them M. Horowitz, J. Plummer, R. Howe 9

10 Circuits with Branches: Constraints on Currents (KCL) i = 1 A i = 1 A The black dot is an electrical connection between the wires i = 1 A What is the value of the current i 2? i 1 = 0.3 A i 2 =? M. Horowitz, J. Plummer, R. Howe 10

11 If You Think of Charge as a Fluid Current: i Current is then fluid flow Current constraints are then about fluid conservation 5 V Voltage Source Device The fluid in any object is constant But we know that a fluid doesn t move unless it is pushed What pushes charge to make it move? A Voltage Source M. Horowitz, J. Plummer, R. Howe 11

12 Electrical Voltage Current: i Voltage is a measure of the potential energy per unit charge It is measured in Volts Which has the units of Joules per Coulomb. 5 V Voltage Source Device The charge on the higher energy side will move through an external path (a wire) to neutralize the negative charge on the other side of the device. This causes the charge to flow in the wire, as well as through the device. M. Horowitz, J. Plummer, R. Howe 12

13 What is a Battery? It is a chemical pump for electrons! There is a pair of chemical reactions that pump electrons from anode to cathode Actually, a battery absorbs electrons at the anode and creates electrons at cathode (with ions moving through the middle), but it has exactly the same effect The battery voltage is the potential energy given to electrons as a result of this pump. The voltage of the battery depends on chemicals Generally either 1.5 V, or multiples Or around 3.5 V (lithium) M. Horowitz, J. Plummer, R. Howe 13

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15 Energy and Power Current: i The battery or power supply provides power to the device. (P = i V) Since energy is conserved, the device does something with this power 5 V Voltage Source Device Resistor turns it into heat LED turns it into light Logic circuit computes something Motor turns it into mechanical energy Pump turns it into potential energy by pumping water uphill M. Horowitz, J. Plummer, R. Howe 14

16 Electrical Devices Current: i We ll learn about many different electrical devices. 5 V Voltage Source Device Resistors Diodes Inductors Capacitors Light Emitting Diodes Motors Transistors M. Horowitz, J. Plummer, R. Howe 15

17 Electrical Devices Current: i Each electrical device responds differently to the voltage and current provided to it. 5 V Voltage Source Device Electrical engineers combine these devices to do interesting and useful things. You ll build and demonstrate several interesting examples in E40M. M. Horowitz, J. Plummer, R. Howe 16

18 Electrical Devices Some Properties Current: i Charge neutral; i.e., charge entering = charge leaving i IN Batteries or power supplies separate charge but the overall device is still charge neutral 5 V Voltage Source Device i OUT The net current into any device is always zero, so i IN = i OUT Current that flows into one end of a wire must flow out the other Often called KCL (Kirchhoff s Current Law) Dissipate power (P = i V) M. Horowitz, J. Plummer, R. Howe 17

19 Electrical Circuit Terminology Current - i Node Device Device 5 V Voltage Source Device Device Devices in Parallel Device Device Wire or Lead Devices in Series M. Horowitz, J. Plummer, R. Howe 18

20 Electrical Circuit Terminology Connected Not Connected Example: M. Horowitz, J. Plummer, R. Howe 19

21 Kirchhoff s Current and Voltage Laws (KCL & KVL) V 1 - i 1 i 2 i 3 V 3 - V 2 - Kirchhoff s Current Law (KCL) states that the current flowing out of any node must equal the current flowing in. So, for example, i 1 = i 2 i 3 Kirchhoff s Voltage Law (KVL) states that the algebraic sum of the voltages around any closed path must be zero. So, for example, V1 V 2 V 3 = 0 M. Horowitz, J. Plummer, R. Howe 20

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24 Labeling (Measuring) Voltage and Current Labels alone don t indicate current direction. It is a combination of the label and the sign You can pick any polarity and direction you want (you ll get the right answer), but convention is the green choices. Answers may be positive or negative. M. Horowitz, J. Plummer, R. Howe 21

25 Example #1: Kirchhoff s Voltage Law (KVL) V 4 V 2 V V 5 V 1 - V V6 - V 1 V 2 - V 3 - V 4 V 6 V 7 = 0 V 1 V 2 - V 3 V 7 = 0 V 4 V 6 = 0 (Check for consistency) Quiz: What can you say about V 4 and V 5? M. Horowitz, J. Plummer, R. Howe 22

26 Example #2: Kirchhoff s Current Law (KCL) i 3 i 1 i 2 i 6 i 4 i 7 i 8 i 5 i 10 i 9 i 1 = i 2 = i 10 i 2 = i 3 i 4 i 5 i 3 = i 6 and i 4 = i 7 i 8 = i 9 = i 10 i 5 M. Horowitz, J. Plummer, R. Howe 23

27 Using KCL and KVL Find the current, and voltages for the circuit below M. Horowitz, J. Plummer, R. Howe 24

28 Getting Back to the Solar Charger: Energy and Power Look inside: See a number of different devices wired together in a circuit: Need to move energy around And that is done with voltage and current M. Horowitz, J. Plummer, R. Howe 25

29 Electrical Power and Energy Voltage is electrical potential energy Volt = Joule/Coulomb Means moving 1 Coulomb of charge up 1V requires 1J Remember definition of an amp? Coulomb/sec i 1V - Power consumed/provided in the electrical component (i)*(v) = 1A * 1V = 1 Joule/sec = 1 Watt of power Often the lost energy is converted to heat Power is the rate of energy transfer i.e. Power = Energy/sec or Energy transferred = (Power)(time) M. Horowitz, J. Plummer, R. Howe 26

30 Getting a Feeling for a Watt Quick physics review Unit of energy Joule = Coulomb Volt Unit of power Watt = Joule/sec = A V If those mean nothing to you You probably know about calories Another unit of energy Calorie = 4 kj (a little c-calorie is only 4 J) 2000 Calories = 10 MJoules 10 MJ/day = 10 7 /( ) ~ 100W (power you put out) 30% is your brain, so your brain uses around 30W M. Horowitz, J. Plummer, R. Howe 27

31 Energy Flow The power associated with the red box is: 1A 5V = 5 W Is the box generating or consuming this power? Every charge that enters, also leaves Charge neutral Does the charge leave with more or less potential energy? More is higher voltage, less is lower voltage If it leaves from the Lower voltage lead energy was lost; The box consumed some energy Higher voltage lead energy was gained; The box supplied energy 1 A 5V - M. Horowitz, J. Plummer, R. Howe 28

32 Energy Flow What generate/dissipates energy The 5 V voltage supply 1 A 5 V The red box - M. Horowitz, J. Plummer, R. Howe 29

33 Find the Power Dissipated In Each Device First figure out which lead has the higher voltage Then figure out whether current flows into or out of that lead 1 A -1 A 1 A 1 A - 5V 2V -5V 1V M. Horowitz, J. Plummer, R. Howe 30

34 Standard Prefixes for SI Units Example, if the unit is a meter M. Horowitz, J. Plummer, R. Howe 31

35 Learning Objectives Charge, Current, Voltage, Electrical Circuits Understand that charge is what makes components electrical Moving charge is called current, and often represented by i Measured in Amps = Coulombs/sec Understand that all components and wires are charge neutral This means that the net charge flowing into an object is 0 KCL - The sum of the currents into an device or wire = 0 The energy that causes the charge to move is called Voltage Measured in Volts = Joules/Coulomb Voltage is a potential energy difference Measured between two nodes M. Horowitz, J. Plummer, R. Howe 32

36 Learning Objectives KCL, KVL, Energy Flow Sum of voltage drop around any loop of devices is always 0 (KVL); sum of currents into any node is always 0 (KCL). The power consumed by a device is always: The current flowing into the terminal multiplied by The voltage across the device. A voltage source is an electrical device where V = V source and the current is determined by the rest of the circuit Learn SI prefixes M. Horowitz, J. Plummer, R. Howe 33

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