1. ELECTRIC CIRCUITS BASICS

2. Electricity Basics Electricity starts with electrons. Every atom contains one or more electrons. Electrons have a negative charge. Simplest model of an atom

3. A Copper Atom Electrons (29 total) Protons (29 total) Valence Ring (Outer Ring) Atoms will have the same number of Electrons in the orbit as there are Protons in the center.

4. But most metals have electrons that can detach from their atoms and move around. These are called free electrons. Gold, silver, copper, aluminum, iron, etc., all have free electrons. The loose electrons make it easy for electricity to flow through these materials, so they are known as electrical conductors. They conduct electricity. The moving electrons transmit electrical energy from one point to another.

5. Electrical Circuits Whether you are using a battery, a fuel cell or a solar cell to produce electricity, there are three things that are always the same:  The source of electricity will have two terminals: a positive terminal and a negative terminal.

6. The source of electricity (whether it is a generator, battery, etc.) will want to push electrons out of its negative terminal at a certain voltage. For example, a AA battery typically wants to push electrons out at 1.5 volts. The electrons will need to flow from the negative terminal to the positive terminal through a copper wire or some other conductor. When there is a path that goes from the negative to the positive terminal, you have a circuit, and electrons can flow through the wire.

7. Basic Electrical Circuits Battery Conductor Resistor (Voltage Source) (Light Bulb) (Wire)

8. + + + - - - + + + - - - + + + - - - + + + - - - Voltage (Pressure) (Electromotive Force) How does electricity flow? What causes electrons to move from atom to atom? Voltage Pushes the electrons

9. + + + - - + + + - - + + + - - + + + - - Voltage (Pressure) (Electromotive Force) - - - - - - - - - - - - -- - - - Voltage Pushes the electrons How does electricity flow? What causes electrons to move from atom to atom?

10. + + + - - + + + - - + + + - - + + + - - - - - - - - - - - - - - -- - - - Voltage Pushes the electrons How does electricity flow? What causes electrons to move from atom to atom?

11. + + + - - + + + - - + + + - - + + + - - Voltage (Pressure) (Electromotive Force) - - - - - - - - - - - - -- - - - The flow of the electrons is referred to as Current How does electricity flow? What causes electrons to move from atom to atom?

12. + + + - - + + + - - + + + - - + + + - - - - - - - - - - - - - - -- - - - How does electricity flow? What causes electrons to move from atom to atom? The flow of the electrons is referred to as Current Electron Flow is measured in Amps

13. Electric Circuits Now that we have the concept of voltage, we can use this concept to understand electric circuits. Just like we can use pipes to carry water, we can use wires to carry electricity. The flow of water through pipes is caused by pressure differences, and the flow is measured by volume of water per time.

14. Electric Circuits In electricity, the concept of voltage will be like pressure. Water flows from high pressure to low pressure; electricity flows from high voltage(higher potential) to low voltage(lower potential). But what flows in electricity? Charges! How do we measure this flow? By Current: current = I =  q /  t UNITS:Amp(ere) = Coulomb / second

15. Electrical Network A combination of various electric elements (Resistor, Inductor, Capacitor, Voltage source, Current source) connected in any manner what so ever is called an electrical network. We may classify circuit elements in two categories, passive and active elements.

16. Active Elements The elements that supply energy to the circuit is called active element. Examples of active elements include voltage and current sources, generators, and electronic devices that require power supplies.

17. Passive Elements The element which receives energy (or absorbs energy) and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L ) field is called passive element.

18. 18 Circuit Symbols

19. Voltage Sources: batteries and power supplies A battery or power supply supplies voltage. This is analogous to what a pump does in a water system. Question: Does a water pump supply water? If you bought a water pump, and then plugged it in (without any other connections), would water come out of the pump? Question: Does the battery or power supply actually supply the charges that will flow through the circuit?

20. Voltage Sources: batteries and power supplies Just like a water pump only pushes water (gives energy to the water by raising the pressure of the water), so the voltage source only pushes the charges (gives energy to the charges by raising the voltage of the charges). Just like a pump needs water coming into it in order to pump water out, so the voltage source needs charges coming into it (into the negative terminal) in order to “pump” them out (of the positive terminal).

21. Circuit Elements In this first part of the course we will consider two of the common circuit elements: resistor capacitor inductor The resistor is an element that “resists” the flow of electricity. The capacitor is an element that stores charge for use later (like a water tower). Inductor stores charge in the form of magnetic field

22. Resistance Current is somewhat like fluid flow. Recall that it took a pressure difference to make the fluid flow due to the viscosity of the fluid and the size (area and length) of the pipe. So to in electricity, it takes a voltage difference to make electric current flow due to the resistance in the circuit.

23. Resistance By experiment we find that if we increase the voltage, we increase the current: V is proportional to I. The constant of proportionality we call the resistance, R: V = I*ROhm’s Law UNITS: R = V/I so Ohm = Volt / Amp.

24. Resistance Just as with fluid flow, the amount of resistance does not depend on the voltage (pressure) or the current (volume flow). The formula V=IR relates voltage to current. If you double the voltage, you will double the current, not change the resistance. As was the case in fluid flow, the amount of resistance depends on the materials and shapes of the wires.

25. Resistance The resistance depends on material and geometry (shape). For a wire, we have: R =  L / A where  is called the resistivity (in Ohm-m) and measures how hard it is for current to flow through the material, L is the length of the wire, and A is the cross-sectional area of the wire. The second lab experiment deals with Ohm’s Law and the above equation.

26. Electrical Power The electrical potential energy of a charge is: PE = q*V. Power is the change in energy with respect to time:Power =  PE /  t. Putting these two concepts together we have: Power =  (qV) /  t = V(  q) /  t = I*V.

27. Electrical Power Besides this basic equation for power: P = I*V remember we also have Ohm’s Law: V = I*R. Thus we can write the following equations for power:P = I 2 *R = V 2 /R = I*V. To see which one gives the most insight, we need to understand what is being held constant.

28. Example When using batteries, the battery keeps the voltage constant. Each D cell battery supplies 1.5 volts, so four D cell batteries in series (one after the other) will supply a constant 6 volts. When used with four D cell batteries, a light bulb is designed to use 5 Watts of power. What is the resistance of the light bulb?

29. Example We know V = 6 volts, and P = 5 Watts; we’re looking for R. We have two equations: P = I*V and V = I*R which together have 4 quantities: P, I, V & R.. We know two of these (P & V), so we should be able to solve for the other two.

30. Example Using the power equation we can solve for I: P = I*V, so 5 Watts = I * (6 volts), or I = 5 Watts / 6 volts = 0.833 amps. Now we can use Ohm’s Law to solve for R: V = I*R, so R = V/I = 6 volts / 0.833 amps = 7.2 .

31. Two basic ways There are two basic ways of connecting two resistors: series and parallel. In series, we connect resistors together like railroad cars: + - + - high Vlow R 1 R 2

32. Series If we include a battery as the voltage source, the series circuit would look like this: R 1 + V bat R 2 Note that there is only one way around the circuit, and you have to go through BOTH resistors in making the circuit - no choice!

33. Parallel In a parallel hook-up, there is a branch point that allows you to complete the circuit by going through either one resistor or the other: you have a choice! High V R 1 Low V R 2

34. Parallel Circuit If we include a battery, the parallel circuit would look like this: + ++ V bat R 1 R 2 - -

35. Formula for Series: To see how resistors combine to give an effective resistance when in series, we can look either at V = I*R, or at R =  L/A. V bat R1R1 R2R2 + - I V1V1 V2V2

36. Formula for Series Using V = I*R, we see that in series the current must move through both resistors. (Think of water flowing down two water falls in series.) Thus I total = I 1 = I 2. Also, the voltage drop across the two resistors add to give the total voltage drop: (The total height that the water fell is the addition of the two heights of the falls.) V total = (V 1 + V 2 ). Thus, R eff = V total / I total = (V 1 + V 2 )/I total = V 1 /I 1 + V 2 /I 2 = R 1 + R 2.

37. Formula for Series Using R =  L/A, we see that we have to go over both lengths, so the lengths should add. The distances are in the numerator, and so the values should add. This is just like in R = V/I (from V = IR) where the V’s add and are in the numerator!

38. Formula for Parallel Resistors The result for the effective resistance for a parallel connection is different, but we can start from the same two places: (Think of water in a river that splits with some water flowing over one fall and the rest falling over the other but all the water ending up joining back together again.) V=I*R, or R =  L/A. + - V bat R1R1 R2R2 I total I1I1 I2I2

39. Formula for Parallel Resistors V=I*R, or R =  L/A For parallel, both resistors are across the same voltage, so V total = V 1 = V 2. The current can go through either resistor, so: I total = (I 1 + I 2 ). Since the I’s are in the denominator, we have: R = V total /I total = V total /(I 1 +I 2 ); or 1/R eff = (I 1 +I 2 )/V total = I 1 /V 1 + I 2 /V 2 = 1/R 1 + 1/R 2.

40. Formula for Parallel Resistors If we start from R =  L/A, we can see that parallel resistors are equivalent to one resistor with more Area. But A is in the denominator (just like I was in the previous slide), so we need to add the inverses: 1/R eff = 1/R 1 + 1/R 2.

41. Review: Resistors: V = IR Power = IV; R =  L/A Series: R eff = R 1 + R 2 Parallel: 1/R eff = 1/R 1 + 1/R 2 series gives largest R eff, parallel gives smallest R eff.

42. Class Problem 42 What is the equivalent resistance of this network of resistors?

43. Capacitance A water tower holds water. A capacitor holds charge. The pressure at the base of the water tower depends on the height (and hence the amount) of the water. The voltage across a capacitor depends on the amount of charge held by the capacitor.

44. Capacitance We define capacitance as the amount of charge stored per volt: C = Q stored /  V. UNITS: Farad = Coulomb / Volt Just as the capacity of a water tower depends on the size and shape, so the capacitance of a capacitor depends on its size and shape. Just as a big water tower can contain more water per foot (or per unit pressure), so a big capacitor can store more charge per volt.

45. Energy Storage Note that previously we had: PE = q*V, and now for a capacitor we have: E = (1/2)*Q*V.

46. Two basic ways There are two basic ways of connecting two capacitors: series and parallel. In series, we connect capacitors together like railroad cars; using parallel plate capacitors it would look like this: + - + - high Vlow V C 1 C 2

47. Series If we include a battery as the voltage source, the series circuit would look like this: C 1 + V bat C 2 Note that there is only one way around the circuit, and you have to jump BOTH capacitors in making the circuit - no choice!

48. Parallel In a parallel hook-up, there is a branch point that allows you to complete the circuit by jumping over either one capacitor or the other: you have a choice! High V C 1 Low V C 2

49. Parallel Circuit If we include a battery, the parallel circuit would look like this: + ++ V bat C 1 C 2

50. Review of Formulas For capacitors in SERIES we have: 1/C eff = 1/C 1 + 1/C 2. For capacitors in PARALLEL we have: C eff = C 1 + C 2. Note that adding in series gives C eff being smaller than the smallest, while adding in parallel gives C eff being larger than the largest!

51. Review: Capacitors: C = Q/V PE = ½CV 2 ; Series: 1/C eff = 1/C 1 + 1/C 2 Parallel: C eff = C 1 + C 2 series gives smallest C eff, parallel gives largest Resistors: V = IR Power = IV; R =  L/A Series: R eff = R 1 + R 2 Parallel: 1/R eff = 1/R 1 + 1/R 2 series gives largest R eff, parallel gives smallest

52. Kirchhoff’s Rules KVL “The sum of potential changes around any closed loop is zero” rise in potential = drop in potential KCL “algebraic sum of all currents entering a node is zero” Current into a junction = current out of a junction 52

53. KCL states that at any node (junction) in a circuit the algebraic sum of currents entering and leaving a node at any instant of time must be equal to zero. Here currents entering(+ve sign) and currents leaving (-ve sign) the node must be assigned opposite algebraic signs. KVL states that in a closed circuit, the algebraic sum of all source voltages must be equal to the algebraic sum of all the voltage drops.