AP Physics 1:

Electrical Circuits

Factors that affect the flow of charges through conductors.

Intro activity

Figure out how to get a Christmas light to light up using the following tools:

• Battery
• Scissors
• Light strand

Minimum requirements:

• Energy difference (+ to -)
• Conducting path
• To get light we need a resistor to allow energy to leave

Electrostatics vs Electrical circuits

We look at 2 stationary charges at a time

Vector addition of forces predicts acceleration of charges/objects through space

We look at the flow of many charges over time

Energy differences through conducting paths predict the flow of charges.

Basic definitions: Current

Current is the rate of charge passing � through a point per second.� Units: Ampere (or amps) 1 A = 1 Coulomb/second

Examples:

What is the current if 2C of charge flow through a wire over the course of 4 seconds?

How many electrons enter a cell phone battery if it charges for 30 minutes with a 0.5 A current?

Basic definitions: Resistance

Resistance is a measurement of how much a component of� a circuit slows the current. Units: Ω (or ohms)

What factors do you think might determine what the resistance of a substance is?

Rank the objects from greatest to least resistance based on the areas and lengths shown �(assuming same materials and temperature)

A

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L

2A

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2L

A

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2L

2A

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L

Albert

Theodore

Bobert

Kevin

Try it

What is the resistance of a 1 m copper wire with a diameter of 6 mm?

Compare the ability to deliver energy

Water model

• water molecules flow naturally from high energy to low (balancing out)�
• A pump produces an energy difference to create a constant flow of molecules

Electric charge model

• Electric charges flow from high energy (closely packed) to low (balancing out)�
• A battery produces an energy difference to create a constant flow of charges

-100

0

Use this comparison to avoid misconceptions:

1. No electrons are “used up” in bulb - it is energy changing form
2. The battery adds energy to the charges to sustain the flow of existing charges.

In honor of Ben Franklin

Ben did not know about protons and electrons.

Conventional current flows �from + to -

We have since learned that �electrons move from - to + �while protons stay put.

This unit will use �conventional current �most of the time.

Drawing circuits using schematic symbols

Simplified circuit diagrams make circuits easier.

Tips: �Draw wires as straight lines with right angles

Draw switches open even if closed.

Worry about connections, not proximity or orientation

Light bulb options

What do volts (J/C) represent?

Electrical Potential (V) tells us about the energy per charge at a given location. Some people call it “Charge Pressure”

Voltage a.k.a. potential difference ΔV is the difference in energy per charge between two locations. When current is flowing it is used to tell the strength of a battery (energy gained per charge across a battery) and to tell about energy loss across resistors (usually given off as heat) through the circuit. It can also be used when current is not flowing

EMF (electromotive force) tells about the energy charges gain from a battery or generator. �In a battery it is the ideal battery voltage, which may not match the voltage if the battery’s ability to keep up with the load is taxed.

How can voltage tracking explain current and voltage changes in series and parallel

In series

In parallel

V

V

Start →

A B

Start →

A B

Use a Voltmeter to measure potential difference

Use an Ammeter to measure current

• Must connect the meter to both sides of the object you want to test (parallel to component)
• Voltmeters have high resistance to prevent drawing current from the circuit

• Must become part of the path or they create a short circuit. (in series with component)
• Ammeters have very low resistance to prevent altering the current within the path

PHET circuit construction kit

Make a prediction: What relationship do you expect between current, and voltage across a lightbulb/battery?

1. Whiteboard a graph showing a prediction.
2. Write procedures for how to test this with a light bulb/resistor

Tools: �Power supply (w/ voltage knob & current reading) �Light bulb, Variable resistor, wires

Lab summary:

Green Resistor vs Light bulb

I

V

I

R

I

V

• Ohm’s law always works to tell the resistance of a resistor given a particular current and voltage drop.
• Ohm’s law can be predictive for “Ohmic resistors” that maintain a constant resistance over the range tested. Double V⇒ double I
• A “Non-Ohmic resistor” changes resistance and therefore the proportionality of Ohm’s law is not useful for predicting future conditions.

Electrical Power P = I ΔV

• Power is measured in Watts (1 W = 1 J/s)
• Power is related to brightness of bulbs
• P=ΔE/t, so we can find the energy used by a device several ways.

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Derivation challenge: generate an expression and derive the units for

Find P in terms of I and R

Find P in terms of V and R

Find ΔE in terms of P and t

Find ΔE in terms of q and V

Using electrical potential to track energy from batteries in series or in parallel.

In series

In parallel

V

V

Start →

Start →

C

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B

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A

A B C

Equivalent Resistance�R_eq is the value a single resistor would need to have to replace several resistors and maintain the same overall current and voltage drop

In series additional resistors increase equivalent resistance and slow current more

In parallel additional resistors reduce equivalent resistance, adding paths for more current

Using Equivalent Resistance: �Use the equivalent resistance to find the current leaving the battery.

Using Equivalent Resistance in combination circuits: Simplify in chunks to find I_battery

Using Equivalent Resistance in combination circuits: Simplify in chunks to find I_battery

Ways to connect more than one resistor

Series: components share a single path

Parallel: components have independent paths

Use the PHET circuit construction kit in lab mode to practice using ammeters & voltmeters to investigate how adding a 2nd or 3rd bulb affects

• Current leaving the battery
• Current passing through the original bulb
• Voltage drop across each bulb

Gustav Kirchhoff (roughly “keer hahf”) 1845 developed 2 rules

that are expressions of conservation laws �(basic principles=highly likely to be tested)

1. Kirchhoff’s Current Rule

The sum of the currents entering any point (junction)= 0

Tips:

• Shows charge conservation
• Incoming currents are + while outgoing currents are -
• Can be reworded to say �∑I_in = ∑I_out

You try: Write expressions for junctions a and b, then solve for the unknown currents.

• This is conservation of energy
• Can be written as ∑ΔV=0
• Determine if ΔV is + or - for each component by proximity to + on battery
• Can use IR instead of ΔV if given

2. Kirchhoff’s Voltage Rule

The sum of the ΔV in a closed circuit (loop) is equal to zero

Compare resistors within and across each circuit:�a) current passing through, �b) voltage drop and �c) change: swap to all 30 Ω bulbs, compare brightness for each

Sum up a pattern we should be seeing

According to the loop rule, �parallel sections of a circuit will always have the same . . . .

According to the junction rule, �components in series will always have the same . . . .

Challenge: Find the the current in R₁

Consider all your tools: voltage rules, current rules, equivalent resistance, ohm’s law

More likely AP calculations: �1. What is the voltage drop across R2?�

2. What is the potential difference across the battery?

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3. What is the resistance of R3?

AP qualitative/semi-quantitative questions test

• Compare graphs of energy dissipated as a function of time for different resistors (parallel, different R)
• Compare currents at different points in a circuit (series, parallel, combo {ranking task})
• Write current and voltage rule equations
• Combo circuit changes in V or I for single components
• leaving a branch open
• Shorting a branch
• Swapping a resistor

Most likely AP Questions: lab design

May use alternate descriptions of values. Which quantity are they asking about if they discuss . . .

• Comparing the number of electrons entering a circuit component
• Potential energy of electrons while passing through a component
• Energy dissipated by a resistor in a given time (ranking task)

Often ask you to describe procedures to set up data collection.

• Explain orientation and/or use a circuit diagram
• Remember how to use voltmeter and ammeter.
• Often ask you to set up basic verification of ohm’s law, current rule, or voltage rule

EMF & Batteries with internal resistance

EMF (ε) = electromotive force is determined by chemistry of the battery = voltage of ideal battery

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ΔV_terminal may be less due to internal resistance.

Internal resistance of battery plan:

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Draw a fake resistor inside the battery, which receives the total current. Voltage rule and ohm’s law to solve.

Talk graphs

Batteries with internal resistance

The current running through R2 is �0.73 A?

1. Calculate the voltage drop due to R_battery

b) Calculate R_battery

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5 Ω

Practice

A battery with an internal resistance of 4.0 ohms is connected to a 16–ohm and a 20–ohm resistor in series. The current in the 20–ohm resistor is 0.3 amps.

A) What is the emf of the battery?

B) What power is dissipated by the 4–ohm internal resistance of the battery?

C) How much thermal energy is produced in 2 hours?

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Internal resistance investigation plan

Goal: Find the internal resistance of a new AA battery from a graph of data collected using the following materials: �variable resistor, wires, battery, ammeter, voltmeter, switch

Diagram the circuit, what to measure/vary, what to graph, how to interpret graph to find r

What happens to each bulb when the switch is connected. Use at least 1 loop rule or junction rule to explain why.

Bulb 1

Bulb 2

Bulb 3