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Current and Resistance CHAPTER 20

Acknowledgments © 2014 Mark Lesmeister/Pearland ISD Selected graphics from OpenStax College, “Electric Current, Resistance, and Ohm's Law,” and “Circuits, Bioelectricity and DC Instruments”, =col11406/1.7, © 2014 OpenStax College =col11406/1.7 OpenStax College content is licensed under Creative Commons Attribution 3.0 License (CC BY 3.0) Creative Commons Attribution 3.0 License (CC BY 3.0)

ELECTRIC CURRENT SECTION 1

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 + + +

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. © OpenStax College

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 m/s, or a few centimeters/hour. © 2013 M. Lesmeister © OpenStax College

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.

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.

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.

Electricity Direct Current Alternating Current

Example 1:

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 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: - +

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:

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

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RESISTANCE SECTION 2

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

Resistance (R) © OpenStax College

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

Example: 2

What determines resistance? Resistance depends on cross sectional 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. 1a 2 A 1 2

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. What determines resistance?

Superconductors Some materials, when cooled to below a low temperature called the critical temperature, have no resistance. © OpenStax College

Example: 3 The cross sectional area of a 20-gauge wire is 5.2x10 -7 m 2, while that of a 16- gauge wire is 13x10 -7 m 2. If the resistivity of both wires is 1.72 x 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.

Example: 3

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?

Factors that affect resistance

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.

Label the graphs as ohmic and non- ohmic

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 © OpenStax College A

A voltmeter is used to measure voltage. –It is placed in parallel with the circuit. –Its resistance is large. –Its symbol is: © OpenStax College Voltmeters and Ammeters V

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 © OpenStax College

Power dissipated by a resistor The power dissipated by a resistor can be expressed by the following formulas. or

Example 4

DUE ON TUESDAY 3/31 COMPLETE YOUR ELECTRIC FIELD HOCKEY ACTIVITY/LAB - HOMEWORK

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

+ - Electric Circuits

SCHEMATIC DIAGRAMS Section 4

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

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

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

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.

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.

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

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.

Series circuits

Example 5

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

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). Series Circuits

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

Parallel Circuits

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. Parallel Circuits – a note!

Parallel Circuits

Example 6

Parallel Wiring

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Section Check What would happen in the circuit below if one of the light bulbs stopped working?

KIRCHHOFF’S RULES Section 6

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.

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.

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.

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.

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. Parallel Circuits

Circuits Series Parallel Circuits Series Parallel

COMPLEX RESISTOR COMBINATIONS Section 7

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 R eq  Repeat until only one resistance remains – R eq of the circuit  You will use this resistance to calculate the total current in the circuit if not provided.

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

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

20.8 Circuits Wired Partially in Series and Partially in Parallel

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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

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