1. Current and Resistance
CHAPTER 20

2. Acknowledgments © 2014 Mark Lesmeister/Pearland ISD
Selected graphics from OpenStax College, “Electric Current, Resistance, and Ohm's Law,” and “Circuits, Bioelectricity and DC Instruments”, , © 2014 OpenStax College
OpenStax College content is licensed under Creative Commons Attribution 3.0 License (CC BY 3.0)

3. Electric current SECTION 1 Focus- Ask what is meant by “current”?
Objective- Relate the concepts of electric current to the movement of charges.
Electric current

4. Electric Current (I)
Current is the rate of charge movement through a given cross sectional area.
Current is defined in terms of positive charge movement.
Current is measured in Amperes (A).
1 A = 1C/s + + +
Explain-

5. Direction of Current
Currents are caused by the presence of electric fields, which cause charges to start moving and continue moving even in the presence of resistive forces.
The direction of the electric field gives the direction of the current.
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Explain that since electrons move opposite the direction of the field, they move in the opposite direction of the electric current.

6. Drift Velocity
Drift velocity is the net velocity of a charge carrier moving in an electric field.
Drift velocities are very slow.
On the order of 10-5 m/s, or a few centimeters/hour.
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© 2013 M. Lesmeister

7. Electromotive Force and Current
Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur.

8. Types of Current Charges can flow in two ways: Direct current (DC)
Charges continuously flow in one direction and current is constant
ex. Batteries
Current in car electrical systems is direct.

9. Types of Current Alternating current (AC)
Motion of charges continuously
changes in the forward and backward directions
Ordinary household current is ‘AC’.
The frequency of AC in the U.S. is 60 Hz.
(0) What are the types of current?
What type is household current? What is the frequency of it?
What type is used in cars?
What effect will those bumping particles have on current? Will all substances require the same potential difference to get the same current?

10. Electricity
Direct Current
Alternating Current

11. Example 1:
The current in a light bulb is A. How long does it take for a total charge of 1.67 C to pass a point in the wire?
G: Q = 1.67 C, I = A
U: t = ? E: S:
S: = 𝟐 𝒔

12. Sources of Current
In order for current to flow, there must be a potential difference.
Both batteries and generators, maintain a potential difference across their terminals by converting other forms of energy into electrical energy

13. A battery converts chemical energy to electrical energy.
Sources of Current
A battery converts chemical energy to electrical energy.
The symbol of a battery is
A generator converts mechanical energy to electrical energy.
The symbols are: - +
(0) What do we need to get a current to flow?
What units do we use for potential difference? What do we use to make that potential difference?
What is the symbol for a battery? What does it mean?
How do they make electricity for houses?

14. Voltage (V)
This ‘electrical push’ which a battery gives to the current is called the voltage(V). It is measured in volts (V) on a voltmeter
Voltage is also referred to as potential difference
The symbol used to represent voltage is:

15. Voltage (V)
The maximum potential difference across the terminals of the batteries is called the electromotive force (emf).

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17. Resistance SECTION 2 Focus- Ask what is meant by “current”?
Objective- Relate the concepts of electric current to the movement of charges.
Resistance

18. RESISTANCE (R)
The force of the electric field causes the free charges in a wire to move.
The charges would continue to accelerate, but because the charges collide with atoms in the conductor, their motion is impeded

19. Resistance (R)
The resistance of the motion of free charges in a conductor depends on the conductor.
Resistance is the ratio of the potential difference to the current that is produced.
Equation:
SI units: Ohms (Ω) or volt/Ampere (𝑉/𝐴)
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This is a definition of R. It is not derived.

20. Resistors
A resistor is a device that has a known amount of resistance.
A resistor can be used to control the amount of current in a circuit.
The symbol for resistor is
Resistors have a color code that gives their resistance.
Some resistors have a dial that can be used to change resistance.

21. Example: 2 G: 𝑅=19.0 Ω, 𝑉=120 𝑉 U: 𝐼 = ? E: 𝑅= 𝑉 𝐼 S: 𝐼= 𝑉 𝑅 S: 𝟔.𝟑𝟐 𝑨
The resistance of a steam iron is 19.0 Ω. What is the current in the iron when it is connected across a potential difference of 120 V?
G: 𝑅=19.0 Ω, 𝑉=120 𝑉
U: 𝐼 = ?
E: 𝑅= 𝑉 𝐼
S: 𝐼= 𝑉 𝑅
= 120𝑉 19Ω
S: 𝟔.𝟑𝟐 𝑨

22. What determines resistance?
Resistance depends on area.
Conductors with wider cross sections have more room for charges to flow, therefore providing a lower resistance.
Resistance depends on length.
Longer conductors have more resistance. 1 a A 2
Have students measure the resistance of a piece of Playdough formed into a short, wide cylinder, and then the resistance of a long, thing cylinder. 1 2

23. What determines resistance?
Resistance depends on the material.
Some materials have more free charges to carry a current.
The resistivity (ρ) is a measure of the resistance to the flow of charges of a material at a given temperature.
Temperature – Higher temperatures result in greater resistance.

24. Superconductors
Some materials, when cooled to below a low temperature called the critical temperature, have no resistance.
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25. Example: 3
The instructions for an electric lawn mower suggest that a 20-gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances. The cross sectional area of a 20-gauge wire is 5.2x10-7m2, while that of a 16-gauge wire is 13x10-7m2. If the resistivity of both wires is 1.72 x 10-8 Ω.m. Determine the resistance of the following:
(a) 35 m of 20-gauge copper wire and
(b) 75 m of 16-gauge copper wire.

26. Example: 3
G: 𝑙1=35𝑚, 𝐴1= 5.2 ×10−7𝑚2 , 𝑙2=75𝑚, 𝐴2= 13×10−7𝑚2, 𝜌= 1.72 × 10−8 Ω.𝑚
U: 𝑅1 𝑎𝑛𝑑 𝑅2
E: 𝑅= 𝜌 𝑙 𝐴
S: 𝑅=1.72 × 10−8Ω.𝑚× 35𝑚 5.2 ×107𝑚2
𝑅=1.72 × 10−8Ω.𝑚× 75𝑚 13 ×107𝑚2
S: 𝑅1 = 1.16 Ω
𝑅2 = 0.99 Ω

27. 20.5 Alternating Current Conceptual Example: Extension Cords and a Potential Fire Hazard
During the winter, many people use portable electric space heaters to keep warm. Sometimes, however, the heater must be located far from a 120-V wall receptacle, so an extension cord must be used.
However, manufacturers often warn against using an extension cord. If one must be used, they recommend a certain wire gauge, or smaller.
Why the warning, and why are smaller-gauge wires better then larger-gauge wires?

28. Factors that affect resistance

30. Ohm’s Law
Ohm’s Law states that, for many materials, resistance is constant over a wide range of potential differences.
For these materials, a V vs. I graph is a straight line.
Ohm’s Law does not hold for all materials.
These materials are said to be non-ohmic.
(0)What did the straight line graphs of potential difference vs. current show?
(1) What if I put so much current through a wire it melts? Will resistance be constant?
(2) Some objects have different resistances, depending on which way the current is flowing.

31. Ammeters and Voltmeters
An ammeter is used to measure current.
It is placed in series within the circuit.
Its resistance is small.
The symbol used to represent an ammeter is A
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32. Voltmeters and Ammeters
A voltmeter is used to measure voltage.
It is placed in parallel with the circuit.
Its resistance is large.
Its symbol is:
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33. Electric Power
Power is the rate at which energy is transferred, used, or transformed.
Units for Power are Watts (W)
Electric companies measure energy consumed in kiloWatt-hours (kWh)
Power is calculated as follows: a b
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34. Power dissipated by a resistor
The power dissipated by a resistor can be expressed by the following formulas.
We know from Ohm’s Law:
𝑉= 𝐼𝑅 and 𝑃 =𝐼𝑉
Therefore:
𝑃 =𝐼(𝐼𝑅) or 𝑷=𝑰𝟐𝑹
What happens to that energy when current flows through a resistor? We can use definition of resistance to find formulas for power. V= IR, so P = VI = I IR = I2 R. Similarly, I = V/R, so P = V2/R
We know form Ohm’s Law:
𝐼 = 𝑉 𝑅 and 𝑃=𝐼𝑉
Therefore:
𝑃 = 𝑉 𝑅 ×𝑉 or 𝑷 = 𝑽 𝟐 𝑹

35. Example 4 G: 𝑉 = 120 𝑉, 𝑃 = 1320 𝑊 U: 𝑅 = ? E: 𝑃= 𝑉 2 𝑅 S: 𝑅= 𝑉 2 𝑃
An electric space heater is connected across a 120 V outlet. The heater dissipates1320 W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the heater.
G: 𝑉 = 120 𝑉, 𝑃 = 1320 𝑊
U: 𝑅 = ?
E: 𝑃= 𝑉 2 𝑅
S: 𝑅= 𝑉 2 𝑃
𝑅= 𝑉 𝑤
S: 𝟏𝟎.𝟗 𝛀

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37. Electric Circuits By: S.MORRIS 2006
More free powerpoints at

38. Electric Circuits - +

39. Section 4
Schematic Diagrams

40. Electric Circuit
An electric circuit is a set of electrical components that are connected so that they can provide one or more complete paths for the movement of charge

41. Schematic diagrams
Schematic diagrams are representations of electric circuits with standardized symbols representing circuit components

42. Draw the following symbols in your notes
Bulb or lamp
Ammeter
Voltmeter

43. Elements of a complete circuit
A potential difference (voltage) is required in order for charge to flow.
Produced by a battery or generator
A closed circuit is one whose electrons have a complete path from the charge source (battery) and back.

44. Elements of a complete circuit
An open circuit is one whose electrons do not have a complete path back to the charge source. This circuit is interrupted at some point along the path.

45. SERIES CIRCUITS
The components are connected end-to-end, one after the other.
If one bulb ‘dies’ it breaks the whole circuit and all the bulbs go out.

46. Series circuits
Series circuits are like one big loop with only one path for current to flow.
The current is the same at all points in the circuit.
The total voltage in this type of circuit is the sum of the voltage across each component in the circuit.

47. Series circuits
The total current in a series circuit depends on the number of resistors present and the resistance of each resistor.
To find the total current in the circuit, we need to know the total resistance (equivalent resistance – 𝑅𝑒𝑞) in the circuit.
For resistors in series:
𝑅𝑒𝑞 = 𝑅1 + 𝑅2 + 𝑅3 …

48. Series circuits

49. Example 5
A 9.0 V battery is connected to four light bulbs, as shown in the diagram. Find the equivalent resistance for the circuit and the current in the circuit.
G: V = 9.0 V, R1 = 2 Ω, R2 = 4 Ω, R3 = 5 Ω, R4 = 7 Ω
U: Req = ? and I = ?
E: Req = R1 + R2 + R3 + R4 and 𝑅= 𝑉 𝐼
S: Req =
= 18Ω
𝐼= 𝑉 𝑅
𝐼= 9 18
S: Req = 18Ω and I = 0.5 A

50. Section Check
What would happen in this circuit if one of the light bulbs stopped working?
The whole circuit will go out!!

51. Series Circuits
think!
What happens to the light intensity of each lamp in a series circuit when more lamps are added to the circuit?
Answer:
The lamps will become dimmer.
The addition of more lamps results in a higher resistance. This decreases the current in the circuit (and in each lamp).

52. PARALLEL CIRCUITS I
The components are connected side by side and therefore,
the current has a choice of paths.
If one bulb ‘dies’ there is still a complete circuit for the other bulb so it stays on.

53. Parallel Circuits
Parallel circuits have multiple paths for the current to flow.
The current in the circuit is the sum of the current across each resistor
The voltage is the same across each component in the circuit
Equivalent resistance for resistors in parallel:
1 𝑅 𝑒𝑞 = 1 𝑅 𝑅 2
Req is the inverse of the resistances as calculated above

54. Parallel Circuits – a note!
When two resistors are connected in parallel, each receives current from the battery as if the other was not present.
Therefore the two resistors connected in parallel draw more current than does either resistor alone.

55. Parallel Circuits

56. Example 6 E: 1 𝑅 𝑒𝑞 = 1 𝑅 1 + 1 𝑅 2 and 𝑅= 𝑉 𝐼
A 20.0 V battery is connected to two resistors, as shown in the figure below. Find the equivalent resistance for the circuit and the total current in the circuit.
G: V = 20.0 V, R1 = 12.0 Ω, R2 = 8.0 Ω
U: Req = ? and I = ?
E: 𝑅 𝑒𝑞 = 1 𝑅 𝑅 and 𝑅= 𝑉 𝐼
S: 1 𝑅 𝑒𝑞 =
𝑅𝑒𝑞 = =4.8 Ω
𝐼= 𝑉 𝑅 𝐼=
S: Req = 4.8 Ω and I = 4.17 A

57. Parallel Wiring

58. Will not accept late work
Class assignment
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59. Section Check
What would happen in the circuit below if one of the light bulbs stopped working?

60. Section 6
Kirchhoff’s Rules

61. Kirchhoff’s Rules
Gustav Robert Kirchhoff was a German physicist who, in 1845, when he was only 21 years old, formulated two rules that govern electric circuits:
The loop rule
The junction rule
You can use these two rules to analyze complex electric circuits.

62. Kirchhoff’s Rules
Some circuits such as (complex circuits) those whose resisters are wired both in series and in parallel
The electrical wiring in our homes is considered a complex circuit, see below:
A fuse or a circuit breaker is connected in series with numerous outlets which are wired in parallel to one another.

63. Kirchhoff’s Loop Rule
Conservation of energy requires that the net change in potential energy around a complete closed path is zero.
Which means the algebraic sum of the changes in voltage within the circuit equals 0.

64. Kirchhoff’s Junction Rule
If charge is not being stored at any point in a conductor, then the charge flowing into that point must equal the charge flowing out.
At any junction point in a circuit where the current can divide, the sum of the currents into the junction equals the sum of the currents out of the junction.

65. Section Check ~ measuring current
SERIES CIRCUIT 2A
current is the same
at all points in the
circuit. 2A 2A
PARALLEL CIRCUIT
current is shared
between the
components 2A 2A 1A 1A

66. Section Check ~ measuring Voltage
SERIES CIRCUIT
Voltage is shared between the components
PARALLEL CIRCUIT
Voltage is the same in all parts of the circuit

67. Parallel Circuits think!
What happens to the light intensity of each lamp in a parallel circuit when more lamps are added in parallel to the circuit?
Answer:
The light intensity for each lamp remains unchanged. Resistance and current changes for the circuit as a whole, but, no changes occurs to the individual branches in the circuit.

68. answers a) b) 6V 6V 4A 4A 6V 4A 4A 3V 3V 2A 4A 6V 2A

69. Circuits
Series Parallel

70. COMPLEX RESISTOR COMBINATIONS
Section 7
COMPLEX RESISTOR COMBINATIONS

71. Complex Resistor Combinations
When determining the equivalent resistance of a complex circuit, you must:
First simplify the circuit into groups of series and parallel resistors
You can redraw the circuit as a group of resistors along one side of the circuit.
Then find the equivalent resistance for each group
You may also redraw the circuit replacing each series and parallel set with the calculated Req
Repeat until only one resistance remains – Req of the circuit
You will use this resistance to calculate the total current in the circuit if not provided.

72. Example Problem #7
Determine the equivalent resistance of the complex circuit shown in the Figure 
Redraw the circuit as a group of resistors
Find the equivalent resistance for each group
Redraw the circuit

73. Example Problem #7 ~ cont.
Repeat until only one resistance is left 
You can now calculate the total current in the circuit
Let us practice

75. 20.8 Circuits Wired Partially in Series and Partially in Parallel

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77. Example Problem #4
Determine the current in and potential difference across the 2.0 Ω resistor highlighted in the figure below.
let us do this together on the board 

78. Class assignment Due By the end of class
Will not accept late work