Lesson#23Lesson#23Topic: Simple CircuitsTopic: Simple Circuits

Objectives: Objectives: (After this class I will be (After this class I will be able to)able to)

1.1. Explain the difference between wiring light Explain the difference between wiring light bulbs in series and in parallelbulbs in series and in parallel

2.2. Describe EMF and terminal voltage of Describe EMF and terminal voltage of batteries.batteries.

3.3. Describe how the difference between EMF Describe how the difference between EMF and terminal voltage can be treated as and terminal voltage can be treated as internal resistance of the battery.internal resistance of the battery.

4.4. Find voltage, current, and resistance for a Find voltage, current, and resistance for a simple circuitsimple circuit

5.5. Explain the loop rule for a single loop.Explain the loop rule for a single loop.

11/13/06

Assignment:

Warm UpWarm Up► A simple series circuit consists of three identical A simple series circuit consists of three identical

lamps powered by a battery. When a wire is lamps powered by a battery. When a wire is connected between points a and b.connected between points a and b.

1.1. What happens to the brightness of lamp 3? What happens to the brightness of lamp 3?

2.2. Does current in the circuit increase, decrease, or Does current in the circuit increase, decrease, or remain the same? remain the same?

3.3. What happens to the brightness of lamps 1 and What happens to the brightness of lamps 1 and 2?2?

4.4. Does the voltage drop across lamps 1 and 2 Does the voltage drop across lamps 1 and 2 increase, decrease, or remain the same?increase, decrease, or remain the same?

5.5. Is the power dissipated by the circuit increased, Is the power dissipated by the circuit increased, decreased, or does it remain the same?decreased, or does it remain the same?

a

b

Series vs. Parallel CircuitsSeries vs. Parallel Circuits► Light bulbs wired in series are lined up one Light bulbs wired in series are lined up one

right after the other.right after the other.► The current throughout the circuit remains The current throughout the circuit remains

the same. the same. ► The circuit makes a single loop from the The circuit makes a single loop from the

positive terminal of the battery to the positive terminal of the battery to the negative terminal.negative terminal.

► Light bulbs wired in parallel are each Light bulbs wired in parallel are each individually connected to the battery individually connected to the battery terminals.terminals.

► The current is then split and divided The current is then split and divided amongst each light bulb. amongst each light bulb.

Series vs. Parallel CircuitsSeries vs. Parallel Circuits► The voltage drop across identical light The voltage drop across identical light

bulbs in series is divided evenly among bulbs in series is divided evenly among each bulb. each bulb.

► The voltage drop across identical light The voltage drop across identical light bulbs in parallel is equal to the original bulbs in parallel is equal to the original voltage of the battery. voltage of the battery.

► Batteries wired in series add voltage (or Batteries wired in series add voltage (or subtract if are reversed)subtract if are reversed)

► Batteries wired in parallel do not add.Batteries wired in parallel do not add.► Two batteries in parallel would light the Two batteries in parallel would light the

bulb about the same as one battery by bulb about the same as one battery by itself. itself.

► Possibly only slightly brighter due to Possibly only slightly brighter due to internal resistance.internal resistance.

EMFEMF► Batteries are rated by the voltage difference Batteries are rated by the voltage difference

between terminals, but when current begins to between terminals, but when current begins to flow between terminals, the voltage drops.flow between terminals, the voltage drops.

► This is similar to what happens in water pipes This is similar to what happens in water pipes when you turn on a faucet.when you turn on a faucet.

► The water pressure is larger when the faucet is The water pressure is larger when the faucet is closed than when the water is running.closed than when the water is running.

► The plumbing cannot maintain the same The plumbing cannot maintain the same pressure as the water is removed.pressure as the water is removed.

► The more water that flows (current) the lower The more water that flows (current) the lower the pressure becomes.the pressure becomes.

► The voltage across the battery terminals goes The voltage across the battery terminals goes down as current is drawn.down as current is drawn.

► The more current drawn, the more the drop in The more current drawn, the more the drop in voltage.voltage.

EMFEMF► Technically, the chemical reactions in the Technically, the chemical reactions in the

battery responsible for producing the electric battery responsible for producing the electric potential energy cannot proceed quickly enough potential energy cannot proceed quickly enough to maintain the potential difference. to maintain the potential difference.

► The initial voltage that the battery is rated at for The initial voltage that the battery is rated at for when there is no current is its when there is no current is its EMF.EMF.

► The actual voltage between terminals when the The actual voltage between terminals when the circuit is closed is the circuit is closed is the terminal voltage.terminal voltage.

► The more current drawn from the battery, the The more current drawn from the battery, the smaller the terminal voltage.smaller the terminal voltage.

Internal ResistanceInternal Resistance► What is typically done when quantifying the What is typically done when quantifying the

properties of circuits is to measure the properties of circuits is to measure the internal internal resistanceresistance of the battery. of the battery.

► The difference in voltage between the EMF and The difference in voltage between the EMF and the terminal voltage can be treated as a tiny the terminal voltage can be treated as a tiny resistor located within the battery.resistor located within the battery.

► We can then say that the EMF is the actual We can then say that the EMF is the actual voltage of the battery.voltage of the battery.

► And that there is an internal resistance that And that there is an internal resistance that causes a voltage drop as soon as the circuit is causes a voltage drop as soon as the circuit is closed.closed.

► This explains why two batteries in parallel will This explains why two batteries in parallel will light a bulb brighter than a single battery in light a bulb brighter than a single battery in series. series.

► This is because when used in parallel, less This is because when used in parallel, less current needs to be drawn from each battery.current needs to be drawn from each battery.

► With less current, the internal resistance of each With less current, the internal resistance of each battery has less of an effect.battery has less of an effect.

Internal ResistanceInternal Resistance► A typical fresh AA dry cell has an EMF of A typical fresh AA dry cell has an EMF of

1.5V and an internal resistance 1.5V and an internal resistance of .31ohmsof .31ohms

1.1. What is the terminal voltage of the What is the terminal voltage of the battery if the battery is hooked up in battery if the battery is hooked up in series to a resistor such that a current of series to a resistor such that a current of 58mA is measured through the resistor?58mA is measured through the resistor?

2.2. What is the resistance of the resistor?What is the resistance of the resistor?3.3. Suppose the resistor was replaced by a Suppose the resistor was replaced by a

wire of negligible resistance. What wire of negligible resistance. What current will flow through the wire?current will flow through the wire?

Loop RuleLoop Rule► If a circuit contains a single battery and a single If a circuit contains a single battery and a single

resistor it is simple to find the current through the resistor it is simple to find the current through the circuit.circuit.

► For circuits with multiple elements a loop rule needs For circuits with multiple elements a loop rule needs to be applied. to be applied.

► This rule extends from the idea that the voltage This rule extends from the idea that the voltage between a point and itself is zero.between a point and itself is zero.

► As we go around a complete loop in a circuit As we go around a complete loop in a circuit (starting and ending at the same point), we find that (starting and ending at the same point), we find that each element is associated with a voltage across it.each element is associated with a voltage across it.

► Loop Rule:Loop Rule: The sum of all of the voltages across The sum of all of the voltages across each element in the loop as you go around the loop each element in the loop as you go around the loop should equal zero.should equal zero.

Loop Rule ExampleLoop Rule Example► Find the current in the following circuit.Find the current in the following circuit.

8Ω

2Ω

6V

Loop Rule ExampleLoop Rule Example► Find the current in the following circuit.Find the current in the following circuit.

8Ω

2Ω

6V

16V

Lesson #24Lesson #24Topic: Lab: Simple CircuitsTopic: Lab: Simple Circuits

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)1.1. Create a simple series circuit with light bulbs Create a simple series circuit with light bulbs 2.2. Measure the voltage drop and current through a Measure the voltage drop and current through a

light bulb using a multimeter.light bulb using a multimeter.3.3. Create a simple parallel circuit with light bulbsCreate a simple parallel circuit with light bulbs4.4. Compare the changes in voltage and current in a Compare the changes in voltage and current in a

series circuit to a parallel circuit.series circuit to a parallel circuit.5.5. Mechanically create the power needed to generate Mechanically create the power needed to generate

the electricity needed to light four bulbs and make the electricity needed to light four bulbs and make note of the difference in torque when bulbs are note of the difference in torque when bulbs are removed. removed.

11/9/06

Lab Task: Complete the Hewitt lab #91. Make sure all tables are completed and questions are answered.

Assignment: Lab due at the end of the period.

Lesson #25Lesson #25Topic: Multi-loop CircuitsTopic: Multi-loop Circuits

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Describe and draw a schematic of a multi-Describe and draw a schematic of a multi-loop circuitloop circuit

2.2. Pick out single loops from a multiple loop Pick out single loops from a multiple loop schematicschematic

3.3. Write voltage equations for each individual Write voltage equations for each individual looploop

4.4. Solve for multiple unknown currents in Solve for multiple unknown currents in different sections of a circuitdifferent sections of a circuit

11/16/06

Warm Up: Draw a circuit with a 12V battery and 3 resistors wired in parallel with one another. If the resistance of each resistor is 2ohms, 4 ohms, and 6ohms, can we say that the current through each section is the same? How can we predict the current in each section?

Assignment: Holt Physics p757 #43 b, c, d, e

Multi-loop CircuitsMulti-loop Circuits► Most real circuits have multiple loops and Most real circuits have multiple loops and

are much more complicated than the light are much more complicated than the light bulb circuits we have been dealing with.bulb circuits we have been dealing with.

► The complication arises when there are The complication arises when there are different size resistors located at within different size resistors located at within different loops. different loops.

► This means that the current will be different This means that the current will be different for different sections of the circuit.for different sections of the circuit.

► To solve for the current in each section, we To solve for the current in each section, we will have to create multiple loop equations will have to create multiple loop equations to solve for the multiple unknown variables.to solve for the multiple unknown variables.

► To create these equations we will follow the To create these equations we will follow the loop rule, or specifically:loop rule, or specifically:

► Kirchoff’s loop rulesKirchoff’s loop rules

Multiple LoopsMultiple Loops► Consider the following circuit. Consider the following circuit.

► Pick out two loops seen within this circuit.Pick out two loops seen within this circuit.► Then use the loop rule to write an equation for Then use the loop rule to write an equation for

each individual loop.each individual loop.► For this loop there are three unknowns, so you For this loop there are three unknowns, so you

should have at least three equations.should have at least three equations.► Notice that there are three independent loops in Notice that there are three independent loops in

this circuit. The top loop, the bottom loop, and this circuit. The top loop, the bottom loop, and the outer loop.the outer loop.

2Ω

8Ω

4Ω

6V

16V

Itop = ?

Imid = ?

Ibot = ?

Junction RuleJunction Rule► The loop rule can only be used to get two of The loop rule can only be used to get two of

the equations.the equations.► In order to get the third independent equation In order to get the third independent equation

we need to examine a point in the circuit we need to examine a point in the circuit where the current is split or comes back where the current is split or comes back together. together.

► Because current is conserved, we can add up Because current is conserved, we can add up the current from two divided sections to obtain the current from two divided sections to obtain the current from the original source. the current from the original source.

2Ω

8Ω

4Ω

6V

16V

Itop = ?

Imid = ?

Ibot = ?

Itop + Imid = Ibot

Solving for multiple unknownsSolving for multiple unknowns► Use the following schematic and Use the following schematic and

direction of current to create two more direction of current to create two more equations besides the junction rule, and equations besides the junction rule, and solve for each of the unknowns using solve for each of the unknowns using algebraic substitution.algebraic substitution.

2Ω

8Ω

4Ω

6V

16V

Itop = ?

Imid = ?

Ibot = ?

Equations:

SolutionSolution

PracticePracticeA simple circuit is set up as shown. If the ammeter reads 1A, what is the resistance R?

4Ω

1Ω

2Ω

R A7V6

V

Lesson #26Lesson #26Topic: Lab: Predicting ResistanceTopic: Lab: Predicting Resistance

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Build a circuit from a schematicBuild a circuit from a schematic

2.2. Correctly wire a multimeter to measure the Correctly wire a multimeter to measure the current in a section of wire.current in a section of wire.

3.3. Write equations and solve for multiple Write equations and solve for multiple unknown variablesunknown variables

4.4. Compare the calculated prediction of Compare the calculated prediction of resistance to the measured resistance of a resistance to the measured resistance of a light bulb.light bulb.

11/29/06

Lab Task: In addition to the usual lab report, complete the calculations and questions found on the lab sheet.

Assignment: Lab Report due tomorrow. DC Exam Review due Friday.

Lesson #27Lesson #27Topic: Simplifying CircuitsTopic: Simplifying Circuits

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Add resistance of resistors that are Add resistance of resistors that are wired in serieswired in series

2.2. Add resistance of resistors that are Add resistance of resistors that are wired in parallel.wired in parallel.

3.3. Simplify a complex circuit to a simple Simplify a complex circuit to a simple circuit by calculating total resistance. circuit by calculating total resistance.

11/30/06

Warm Up: If you add resistors to a circuit wired in series, will the overall resistance go up or down? What if the circuit and the added resistors were wired in parallel with each other?

Assignment: Holt Physics p755,756 #23, 24, 25, 26, 33

Adding Resistance in SeriesAdding Resistance in Series► When you add resistors to a circuit in series, the When you add resistors to a circuit in series, the

overall resistance of the circuit will overall resistance of the circuit will increaseincrease► This is because the same current is forced This is because the same current is forced

through each resistor through each resistor ► The voltage drop across each resistor is the total The voltage drop across each resistor is the total

voltage divided by each resistor.voltage divided by each resistor.► If the resistance of each resistor is constant, and If the resistance of each resistor is constant, and

the voltage drop per resistor goes down with each the voltage drop per resistor goes down with each resistor added, then the current must drop as resistor added, then the current must drop as well.well.

► Hence, as you add bulbs to a series circuit, bulbs Hence, as you add bulbs to a series circuit, bulbs get dimmer.get dimmer.

► The total resistance of a series circuit is the The total resistance of a series circuit is the simple addition of the resistance of each simple addition of the resistance of each individual resistor.individual resistor.

ntotal RRRRR ....321

PracticePractice►Find the total resistance in the circuit.Find the total resistance in the circuit.►Find the total current drawn from the Find the total current drawn from the

battery.battery.

1Ω

5Ω

2Ω 3Ω 4Ω

7Ω6Ω

7V

Adding Resistance in ParallelAdding Resistance in Parallel► When you add resistors to a circuit in parallel, the When you add resistors to a circuit in parallel, the

overall resistance of the circuit will overall resistance of the circuit will decrease.decrease.► This is because the current is split through each This is because the current is split through each

resistor.resistor.► The voltage drop across each resistor is the same The voltage drop across each resistor is the same

as the total voltage of the circuit.as the total voltage of the circuit.► If the resistance of each resistor is constant, and If the resistance of each resistor is constant, and

the voltage drop per resistor remains the same the voltage drop per resistor remains the same with each resistor added, then the current drawn with each resistor added, then the current drawn from the battery must increase.from the battery must increase.

► If the voltage is held constant and the overall If the voltage is held constant and the overall current increases, then the resistance must drop current increases, then the resistance must drop as bulbs are added.as bulbs are added.

► The total resistance of a parallel circuit is the The total resistance of a parallel circuit is the inverse of the addition of the inverses of each inverse of the addition of the inverses of each individual resistor.individual resistor.

ntotal RRRRR

1....

1111

321

PracticePractice►Find the total resistance in the circuit.Find the total resistance in the circuit.►Find the total current drawn from the Find the total current drawn from the

battery.battery.

1Ω

2Ω

3Ω

6Ω

7V

Simplifying CircuitsSimplifying Circuits►With these addition rules, we can With these addition rules, we can

simplify circuits to a single battery and simplify circuits to a single battery and resistor.resistor.

►This is useful for finding the total This is useful for finding the total voltage, resistance, or current drawn voltage, resistance, or current drawn from a single battery in a circuit.from a single battery in a circuit.

►This cannot be used to solve for the This cannot be used to solve for the current within sections of a parallel current within sections of a parallel circuit. circuit.

PracticePracticeFind the equivalent resistance of circuit and the current drawn from the battery.

4Ω

1Ω

2Ω

8 Ω

8Ω

6V

4Ω