Electric Current & DC Circuits www.njctl.org http://njc.tl/iq - - PDF document

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Electric Current & DC Circuits

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This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others.

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Slide 2 / 99 How to Use this File

· Each topic is composed of brief direct instruction · There are formative assessment questions after every topic denoted by black text and a number in the upper left. > Students work in groups to solve these problems but use student responders to enter their own answers. > Designed for SMART Response PE student response systems. > Use only as many questions as necessary for a sufficient number of students to learn a topic. · Full information on how to teach with NJCTL courses can be found at njctl.org/courses/teaching methods

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Click on the topic to go to that section

· Circuits · Conductors · Resistivity and Resistance · Circuit Diagrams

Electric Current & DC Circuits

· Measurement

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· EMF & Terminal Voltage · Kirchhoff's Rules

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Return to Table of Contents

Circuits

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Slide 5 / 99 Electric Current

Electric Current is the rate of flow of electric charges (charge carriers) through space. More specifically, it is defined as the amount of charge that flows past a location in a material per unit

• time. The letter "I" is the symbol for current.

ΔQ is the amount of charge, and Δt is the time it flowed past the location. The current depends on the type of material and the Electric Potential difference (voltage) across it. ΔQ Δt I =

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Electric Current

A good analogy to help understand Electric Current is to consider water flow. The flow of water molecules is similar to the flow of electrons (the charge carriers) in a wire. Water flow depends on the pressure exerted on the molecules either by a pump or by a height difference, such as water falling

• ff a cliff.

Electric current depends on the "pressure" exerted by the Electric Potential difference - the greater the Electric Potential difference, the greater the Electric Current.

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The current, has the units Coulombs per second. The units can be rewritten as Amperes (A). 1 A = 1 C/s Amperes are often called "amps". ΔQ Δt I =

Electric Current

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Slide 8 / 99 Electric Current

We know that if an Electric Potential difference is applied to a wire, charges will flow from high to low potential - a current. However, due to a convention set by Benjamin Franklin, current in a wire is defined as the movement of positive charges (not the electrons which are really moving) and is called "conventional current." Ben didn't do this to confuse future generations of electrical engineers and students. It was already known that electrical phenomena came in two flavors - attractive and repulsive - Ben was the person who explained them as distinct positive and negative charges.

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Electric Current

He arbitrarily assigned a positive charge to a glass rod that had been rubbed with silk. He could just as easily called it negative - 50/50 chance. The glass rod was later found to have a shortage of electrons (they were transferred to the silk). So if the glass rod is grounded, the electrons will flow from the ground to the rod. The problem comes in how Electric Potential is defined - charge carriers will be driven from high to low potential - from positive to

• negative. For this to occur in the glass rod - ground system, the

conventional current will flow from the rod to the ground - opposite the direction of the movement of electrons.

Slide 10 / 99 Electric Current

To summarize - conventional Electric Current is defined as the movement of positive charge. In wires, it is opposite to the direction of the electron movement. However - in the case of a particle accelerator, where electrons are stripped off of an atom, resulting in a positively charged ion, which is then accelerated to strike a target - the direction of the conventional current is the same as the direction of the positive ions!

Slide 11 / 99 Circuits

An electric circuit is an external path that charges can follow between two terminals using a conducting material. For charge to flow, the path must be complete and unbroken. An example of a conductor used to form a circuit is copper wire. Continuing the water analogy, one can think of a wire as a pipe for charge to move through.

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1 12 C of charge passes a location in a circuit in 10

• seconds. What is the current flowing past the point?

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1 12 C of charge passes a location in a circuit in 10

• seconds. What is the current flowing past the point?

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Answer

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2 A circuit has 3 A of current. How long does it take 45 C

• f charge to travel through the circuit?

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2 A circuit has 3 A of current. How long does it take 45 C

• f charge to travel through the circuit?

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Answer

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3 A circuit has 2.5 A of

• current. How much charge travels

through the circuit after 4s?

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3 A circuit has 2.5 A of

• current. How much charge travels

through the circuit after 4s?

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Answer

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Batteries

Positive Terminal Negative Terminal Each battery has two terminals which are conductors. The terminals are used to connect an external circuit allowing the movement of charge. Batteries convert chemical energy to electrical energy which maintains the potential difference. The chemical reaction acts like an escalator, carrying charge up to a higher voltage.

Click here for a Battery Voltage Simulation from PhET

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Slide 16 / 99 Reviewing Basic Circuits

The circuit cannot have gaps. The bulb had to be between the wire and the terminal. A voltage difference is needed to make the bulb light. The bulb still lights regardless of which side of the battery you place it on. As you watch the video,observations and the answers to the questions below. What is going on in the circuit? What is the role of the battery? How are the circuits similar? different?

Click here for video using the circuit simulator from PhET

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The battery pushes current through the circuit. A battery acts like a pump, pushing charge through the circuit. It is the circuit's energy source. Charges do not experience an electrical force unless there is a difference in electrical potential (voltage). Therefore, batteries have a potential difference between their terminals. The positive terminal is at a higher voltage than the negative terminal.

Batteries and Current

How will voltage affect current?

click here for a video from Veritasium's Derek on current

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Return to Table of Contents

Conductors

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Slide 19 / 99 Conductors

Some conductors "conduct" better or worse than others. Reminder: conducting means a material allows for the free flow of electrons. The flow of electrons is just another name for current. Another way to look at it is that some conductors resist current to a greater or lesser extent. We call this resistance, R. Resistance is measured in ohms which is noted by the Greek symbol omega (Ω)

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How will resistance affect current?

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Slide 20 / 99 Current vs Resistance & Voltage

Raising resistance reduces current. Raising voltage increases current. We can combine these relationships in what we call "Ohm's Law". Another way to write this is that: OR V = IR

V R I =

V I R = You can see that one # = V A

click here for a Veritasium music video on electricity

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4 A flashlight has a resistance of 25 # and is connected by a wire to a 120 V source of voltage. What is the current in the flashlight?

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4 A flashlight has a resistance of 25 # and is connected by a wire to a 120 V source of voltage. What is the current in the flashlight?

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Answer

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5 How much voltage is needed in order to produce a 0.70 A current through a 490 # resistor?

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6 What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 V is applied across it?

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6 What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 V is applied across it?

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Answer

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Electrical Power

Power is defined as work per unit time if W = QV then substitute: if then substitute: P = W t P = QV t I = Q t P = IV What happens if the current is increased? What happens if the voltage is decreased?

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Slide 25 / 99 Electrical Power

Let's think about this another way... The water at the top has GPE & KE. As the water falls, it loses GPE and the wheel gets turned, doing work.When the water falls to the bottom it is now slower, having done work.

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Slide 26 / 99 Electrical Power

Electric circuits are similar. A charge falls from high voltage to low voltage. In the process of falling energy may be used (light bulb, run a motor, etc). What is the unit of Power?

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Electrical Power

How can we re-write electrical power by using Ohm's Law? P = IV (electrical power) I = V R (Ohm's Law) P = VV R P = V2 R

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Is there yet another way to rewrite this? P = IV (electrical power) V = I R (Ohm's Law) P = I(IR) P = I2R We can substitute this into Power I = V can be rewritten as V = IR. R

Electrical Power

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D C AAA AA 9 V 1.5 V D, C, AA, & AAA have the same voltage, however they differ in the amount of power they deliver. For instance, D batteries can deliver more current and therefore more power.

Batteries

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7 A toy car's electric motor has a resistance of 17 # ; find the power delivered to it by a 6-V battery.

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7 A toy car's electric motor has a resistance of 17 # ; find the power delivered to it by a 6-V battery.

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Answer

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8 What is the power consumption of a flash light bulb that draws a current of 0.28 A when connected to a 6 V battery?

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8 What is the power consumption of a flash light bulb that draws a current of 0.28 A when connected to a 6 V battery?

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Answer

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9 A 30Ω toaster consumes 560 W of power: how much current is flowing through the toaster?

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10 When 30 V is applied across a resistor it generates 600 W of heat: what is the magnitude of its resistance?

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10 When 30 V is applied across a resistor it generates 600 W of heat: what is the magnitude of its resistance?

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Answer

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Return to Table of Contents

Resistivity and Resistance

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"Pipe" size

How could the wire in the circuit affect the current? If wire is like a pipe, and current is like water that flows through the pipe... if there were pipes with water in them, what could we do to the pipes to change the speed of the water (the current)?

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Slide 36 / 99 "Pipe" size

How could the wire in the circuit affect the current? If wire is like a pipe, and current is like water that flows through the pipe... if there were pipes with water in them, what could we do to the pipes to change the speed of the water (the current)?

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Answer change the cross-sectional area of the pipe making it bigger will allow more water to flow change the length of the pipe increasing the length will increase the time it takes for the water to get to the end of its trip

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Resistivity & Resisitance

Every conductor "conducts" electric charge to a greater or lesser extent. The last example also applies to conductors like copper wire. Decreasing the length (L) or increasing the cross-sectional area (A) would increase conductivity. Also, the measure of a conductor's resistance to conduct is called its resistivity. Each material has a different resistivity. Resistivity is abbreviated using the Greek letter rho ( #). Combining what we know about A, L, and ρ, we can find a conductor's total resistance. R = #L A

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Resistivity & Resisitance

Resistance, R, is measured in Ohms (Ω). Ω is the Greek letter Omega. Cross-sectional area, A, is measured in m2 Length, L, is measured in m Resistivity, ρ, is measured in Ωm R = #L A How can we define A for a wire?

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Resisitance

What is the resistance of a good conductor? Low; low resistance means that electric charges are free to move in a conductor. # = RA L

Click here for a PhET simulation about Resistance

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Resistivities of Common Conductors Resistivity (10-8 Ωm) Material

Silver Copper Gold Aluminum Tungsten Iron Platinum Mercury Nichrome 1.59 1.68 2.44 2.65 5.60 9.71 10.6 98 100

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11 Rank the following materials in order of best conductor to worst conductor.

A Iron, Copper, Platinum B Platinum, Iron, Copper C Copper, Iron, Platinum

Resistivity (10-8 Ωm) Material

Silver Copper Gold Aluminum Tungsten Iron Platinum Mercury Nichrome 1.59 1.68 2.44 2.65 5.60 9.71 10.6 98 100 http://njc.tl/nr

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11 Rank the following materials in order of best conductor to worst conductor.

A Iron, Copper, Platinum B Platinum, Iron, Copper C Copper, Iron, Platinum

Resistivity (10-8 Ωm) Material

Silver Copper Gold Aluminum Tungsten Iron Platinum Mercury Nichrome 1.59 1.68 2.44 2.65 5.60 9.71 10.6 98 100 http://njc.tl/nr

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Answer

C

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12 What is the resistance of a 2 m long copper wire whose cross-sectional area of 0.2 mm2?

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13 An aluminum wire with a length of 900 m and cross- sectional area of 10 mm 2 has a resistance of 2.5 # . What is the resistivity of the wire?

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13 An aluminum wire with a length of 900 m and cross- sectional area of 10 mm 2 has a resistance of 2.5 # . What is the resistivity of the wire?

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Answer

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14 What diameter of 100 m long copper wire would have a resistance of 0.10 # ?

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14 What diameter of 100 m long copper wire would have a resistance of 0.10 # ?

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Answer

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15 What is the length of a 10 Ω copper wire whose diameter is 3.2 mm?

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15 What is the length of a 10 Ω copper wire whose diameter is 3.2 mm?

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Answer

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16 The length of a copper wire is cut to half. By what factor does the resistance change?

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A 1/4 B 1/2 C 2 D 4

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16 The length of a copper wire is cut to half. By what factor does the resistance change?

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A 1/4 B 1/2 C 2 D 4

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Answer

B

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17 The radius of a copper wire is doubled. By what factor does the resistivity change?

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A 1/4 B 1/2 C 1 D 2

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17 The radius of a copper wire is doubled. By what factor does the resistivity change?

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A 1/4 B 1/2 C 1 D 2

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Answer

C

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Return to Table of Contents

Circuit Diagrams

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Circuit Diagrams

Drawing realistic pictures of circuits can be very difficult. For this reason, we have common symbols to represent each piece. Resistor Battery Wire *Note: Circuit diagrams do not show where each part is physically located.

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Circuit Diagrams

Draw a simple circuit that has a 9 V battery with a 3 Ω resistor across its terminals. What is the magnitude and direction of the current? Conventional current flows from the positive terminal to the negative terminal.

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Circuit Diagrams

Draw a simple circuit that has a 9 V battery with a 3 Ω resistor across its terminals. What is the magnitude and direction of the current? Conventional current flows from the positive terminal to the negative terminal.

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Answer

R = 3# V = 9 V I I = 3A

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There are two ways to add a second resistor to the circuit.

R1 R2 V R1 R2 V

Series Parallel All charges must move through both resistors to get to the negative terminal. Charges pass through either R1 or R2 but not both.

Circuit Diagrams

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Are the following sets of resistors in series or parallel? R1 R2 V R1 R2 V

Circuit Diagrams

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Are the following sets of resistors in series or parallel? R1 R2 V R1 R2 V

Circuit Diagrams

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Answer

Series Parallel

The "test" is to trace the shortest route around the circuit. The resistors found on the same route are in series; those not found on the same route are in parallel to those that were.

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Equivalent Resistance

Resistors and voltage from batteries determine the current. Circuits can be redrawn as if there were only a single resistor and battery. By reducing the circuit this way, the circuit becomes easier to study. The process of reducing the resistors in a circuit is called finding the equivalent resistance (R

eq).

R1 R2 V

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Slide 53 / 99 Series Circuits: Equivalent Resistance

What happens to the current in the circuit to the right?

R1 R2 V

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Slide 54 / 99 Series Circuits: Equivalent Resistance

What happens to the current in the circuit to the right?

R1 R2 V

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Answer The current passing through all parts of a series circuit is the

• same. For example: I = I1 = I2

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Series Circuits: Equivalent Resistance

What happens to the voltage as it moves around the circuit?

R1 R2 V

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Slide 55 / 99 Series Circuits: Equivalent Resistance

What happens to the voltage as it moves around the circuit?

R1 R2 V

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Answer The sum of the voltage drops across each of the resistors in a series circuit equals the voltage

• f the battery.

For example: V = V1 + V2

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If V = V1 + V2 + V3 + ... IR = I1R1 + I2R2 + I3R3 IR = IR1 + IR2 + IR3 Req = R1 + R2 + R3 + ...

To find the equivalent resistance (R

eq) of a series circuit,

add the resistance of all the resistors.If you add more resistors to a series circuit, what happens to the resistance?

Series Circuits: Equivalent Resistance

substitute Ohm's Law solved for V is: V = IR but since current (I) is the same everywhere in a series circuit, I = I1 = I2 = I3

Now divide by I

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18 What is the equivalent resistance in this circuit?

R1 = 5# R2 = 3# V = 9 V

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18 What is the equivalent resistance in this circuit?

R1 = 5# R2 = 3# V = 9 V

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Answer Resistors in series:

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19 What is the total current at any spot in the circuit?

R1 = 5# R2 = 3# V = 9 V

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19 What is the total current at any spot in the circuit?

R1 = 5# R2 = 3# V = 9 V

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Answer Resistors in series:

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20 What is the voltage drop across R1?

R1 = 5# R2 = 3# V = 9 V

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20 What is the voltage drop across R1?

R1 = 5# R2 = 3# V = 9 V

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Answer

Resistors in series: Net Current/equal everywhere: Voltage Drop across R1:

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hint: A good way to check your work is to see if the voltage drop across all resistors equals the total voltage in the circuit.

21 What is the voltage drop across R2?

R1 = 5# R2 = 3# V = 9 V

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hint: A good way to check your work is to see if the voltage drop across all resistors equals the total voltage in the circuit.

21 What is the voltage drop across R2?

R1 = 5# R2 = 3# V = 9 V

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Answer

Net Current/equal everywhere: Resistors in series: Voltage Drop across R2:

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22 How much power is used by R1?

R1 = 5# R2 = 3# V = 9 V

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Slide 61 (Answer) / 99 Parallel Circuits: Equivalent Resistance

What happens to the current in the circuit to the right?

R1 R2 V

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Slide 62 / 99 Parallel Circuits: Equivalent Resistance

What happens to the current in the circuit to the right?

R1 R2 V

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Answer The sum of the currents through each of the resistors in a parallel circuit equals the current

• f the battery.

For example: I = I1 + I2

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Parallel Circuits: Equivalent Resistance

What happens to the voltage as it moves around the circuit?

R1 R2 V

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Slide 63 / 99 Parallel Circuits: Equivalent Resistance

What happens to the voltage as it moves around the circuit?

R1 R2 V

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Answer The voltage across all the resistors in a parallel circuit is the same. For example: V = V1 = V2

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If I = I

1 + I2 + I3

V1 R1 V R V3 R3 V2 R2 + + = V R1 V R V R3 V R2 + + = 1 R1 V R 1 R3 1 R2 + + = V(

(

1 R1 1 Req 1 R3 1 R2 + + =

If you add more resistors in parallel, what will happen to the resistance of the circuit? Rewrite Ohm's Law for I and substitute for each resistor Also, since V = V1 = V2 = V3 so we can substitute V for any other voltage Voltage is a common factor, so factor it

• ut!

Divide by V to eliminate voltage from the equation.

Parallel Circuits: Equivalent Resistance

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23 What is the equivalent resistance in the circuit?

R1 = 3# R2 = 6# V = 18V

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23 What is the equivalent resistance in the circuit?

R1 = 3# R2 = 6# V = 18V

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Answer

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24 What is the voltage at any spot in the circuit?

R1 = 3# R2 = 6# V = 18V

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24 What is the voltage at any spot in the circuit?

R1 = 3# R2 = 6# V = 18V

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Answer 18 V

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25 What is the current through R1?

R1 = 3# R2 = 6# V = 18V

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25 What is the current through R1?

R1 = 3# R2 = 6# V = 18V

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Answer

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26 What is the current through R2?

R1 = 3# R2 = 6# V = 18V

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26 What is the current through R2?

R1 = 3# R2 = 6# V = 18V

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Answer

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27 What is the power used by R1?

R1 = 3# R2 = 6# V = 18V

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27 What is the power used by R1?

R1 = 3# R2 = 6# V = 18V

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Answer Power used by R1:

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28 What is the power used by R2?

R1 = 3# R2 = 6# V = 18V

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28 What is the power used by R2?

R1 = 3# R2 = 6# V = 18V

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Answer Power used by R2:

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29 What is the total current in this circuit ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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29 What is the total current in this circuit ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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Answer

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30 What is the voltage drop across the third resistor ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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30 What is the voltage drop across the third resistor ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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Answer

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31 What is the current though the first resistor ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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31 What is the current though the first resistor ?

R1 = 3# R2 = 6# V = 18V R3 = 4#

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Answer

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Measurement

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Slide 74 / 99 Voltmeter

Voltage is measured with a voltmeter. Voltmeters are connected in parallel and measure the difference in potential between two points. Since circuits in parallel have the same voltage, and a voltmeter has very high resistance, very little current passes through it. This means that it has little effect on the circuit.

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Slide 75 / 99 Ammeter

Current is measured using an ammeter. Ammeters are placed in series with a circuit. In order to not interfere with the current, the ammeter has a very low resistance.

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Multimeter

Although there are separate items to measure current and voltage, there are devices that can measure both (one at a time). These devices are called multimeters.Multimeters can also measure resistance.

Click here for a PhET simulation on circuits

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Slide 77 / 99

L

32 A group of students prepare an experiment with electric

• circuits. Which of the following diagrams can be used to

measure both current and voltage?

A B C D E

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Slide 78 / 99

L

32 A group of students prepare an experiment with electric

• circuits. Which of the following diagrams can be used to

measure both current and voltage?

A B C D E

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Answer E

Slide 78 (Answer) / 99

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EMF & Terminal Voltage

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Slide 79 / 99 Electromotive Force

Req E r _ + A battery is a source of voltage AND a resistor. Each battery has a source of electromotive force and internal resistance. Electromotive force (EMF) is the process that carries charge from low to high voltage. Another way to think about it is that EMF is the voltage you measure when no resistance is connected to the circuit.

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Slide 80 / 99

Req E r _ + Terminal voltage (VT) is the voltage measured when a voltmeter is across its terminals. If there is no circuit attached, no current flows, and the measurement will equal the EMF.

Electromotive Force

If however a circuit is attached, the internal resistance will result in a voltage drop, and a smaller terminal voltage. (E - Ir)

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Req E r _ + We say that the terminal voltage is: VT = E - Ir Maximum current will occur when there is zero external current. When solving for equivalent resistance in a circuit, the internal resistance of the battery is considered a series resistor. REQ = Rint + Rext

Terminal Voltage

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Slide 82 / 99

33 When the switch in the circuit below is open, the voltmeter reading is referred to as:

A EMF B Current C Power D Terminal Voltage E Restivity

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Slide 83 / 99

33 When the switch in the circuit below is open, the voltmeter reading is referred to as:

A EMF B Current C Power D Terminal Voltage E Restivity

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Answer A

Slide 83 (Answer) / 99

34 When the switch in the circuit below is closed, the voltmeter reading is referred to as:

A Terminal Voltage B EMF C Current D Resistance E Power

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Slide 84 / 99

34 When the switch in the circuit below is closed, the voltmeter reading is referred to as:

A Terminal Voltage B EMF C Current D Resistance E Power

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Answer A

Slide 84 (Answer) / 99

35 A 6V battery, whose internal resistance 1.5 Ω is connected in series to a light bulb with a resistance

• f 6.8 Ω. What is the current in the circuit?

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Slide 85 / 99

Slide 85 (Answer) / 99

36 A 6V battery, whose internal resistance 1.5Ω is connected in series to a light bulb with a resistance

• f 6.8Ω. What is the terminal voltage of the battery?

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Slide 86 / 99 Slide 86 (Answer) / 99

37 A 25 Ω resistor is connected across the terminals

• f a battery whose internal resistance is 0.6 Ω.

What is the EMF of the battery if the current in the circuit is 0.75 A?

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Slide 87 / 99 Slide 87 (Answer) / 99

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Kirchhoff's Rules

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Slide 88 / 99

Up until this point we have been analyzing simple circuits by combining resistors in series and parallel and using Ohm's law. This works for simple circuits but in order analyze more complex circuits we need to use Kirchhoff's Rules which are based on the laws of conservation of charge and energy.

Kirchhoff's Rules Slide 89 / 99

Kirchhoff's First rule, or junction rule is based on the law of conservation of charge. It states: At any junction point, the sum of all currents entering the junction point must equal the sum of all the currents exiting the junction. For example, I1 + I2 = I3

Kirchhoff's Rules

I1 I2 I3

Slide 90 / 99

Kirchhoff's Second rule , or loop rule is based on the law of conservation of energy. It states: The sum of all changes in potential around any closed path must equal zero. For example, The sum of the voltage drops is equal to the voltage across the battery. V - V1 - V2 =0 OR V = V 1 + V2

Kirchhoff's Rules

V V1 V2

Slide 91 / 99

• 1. Label + and - for each battery.
• 2. Label the current in each branch with a symbol and an
• arrow. (Don't worry about the direction of the arrow. It it's

incorrect the solution will be negative.)

• 3. Apply the junction rule to each junction. You need as many

equations as there are unknowns. (You can also use Ohm's Law to reduce the number of unknowns.)

• 4. Apply the loop rule for each loop. (Pay attention to signs.

For a resistor, the potential difference is negative. For a battery the potential difference is positive.)

• 5. Solve the equations algebraically.

Problem Solving with Kirchhoff's Rules Slide 92 / 99

Find the unknowns in the following circuit:

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# V3 = 1.87 V I2 = 2.6 A

Slide 93 / 99 Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

First, label + and - for each battery.

Slide 94 / 99

Next, label the current in each branch with a symbol and an arrow.

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

I3 I4 I I1

Slide 95 / 99

Next, apply the junction rule to each junction.

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

I3 I4 I I1

Slide 96 / 99

Next, apply the junction rule to each junction.

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

I3 I4 I I1

[This object is a pull tab]

Answer I = I3 + I4 = I2 I1 = I3

Slide 96 (Answer) / 99

Next, apply the loop rule to each loop.

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

I3 I4 I1 I

I = I3 + I4 I = I2 I1 = I3

Slide 97 / 99

Next, apply the loop rule to each loop.

Problem Solving with Kirchhoff's Rules

R1 = 5# R2 = 3#

V = 12 V

R3 = ? R4 = 2# I2 = 2.6 A V3 = 1.87 V

+

_

I3 I4 I1 I

I = I3 + I4 I = I2 I1 = I3

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Answer V = V3 + V1 + V2 V = V4 + V2 V1 + V3 = V4

Slide 97 (Answer) / 99 Problem Solving with Kirchhoff's Rules

V = V3 + V1 + V2 V = V4 + V2 V1 + V3 = V4 I = I3 + I4 I = I2 I1 = I3

Current (Amps) Voltage (Volts) Resistance (Ohms) R1 5 R2 2.6 3 R3 1.87 R4 2 Total 12

List the givens and use ohm's law to solve for the unknowns.

Answer

Slide 98 / 99

Find the unknowns in the following circuit:

Problem Solving with Kirchhoff's Rules

V = 120 V R1 = 10 # I1 = 7 A V1 = 70 V R3 = 2 # I3 = 10 A V3 = 20 V R4 = 3 # I4 = 10 A V4 = 30 V R2 = 23 # I2 = 3 A V2 = 70 V ? ? ? ? ? ? ?

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