# Electricity: Coulomb's Law and Circuits

Electricity: Coulombs Law and Circuits Vocabulary Electric charge (q) exists due to excess or deficient electrons on an object. Charge comes in two kinds: positive and negative. The unit of charge is the coulomb.

Electric current (I) is the flow of (positive) charge per second. The unit of current are amperes. One ampere means one coulomb of charge flowing per second. Vocabulary Contd.

Resistance (R) tells how difficult it is for charge to flow through a circuit element. measured in ohms ()) Resistivity () is a property of a material, ) is a property of a material, which implies what the resistance would be of a meter-cube bit of that material. Voltage (V) is electrical potential energy per

coulomb of charge. Vocabulary Contd. Resistors are connected in series if they are connected in a single path Resistors are connected in parallel if the path for current divides, then comes immediately back together.

Electricity AP wants you to learn two aspects of electricity: 1. How charged objects apply forces to each other in isolation, as when a balloon sticks to the wall. 2. Know about circuits, in which gazillions of

submicroscopic flowing charges produce effects that can be measured and observed. Electric Charge All matter is made up of three types of particles: protons, neutrons, and electrons Protons have an intrinsic property called positive charge

Neutrons dont contain any charge Electrons have a property called negative charge Coulomb The unit of charge (C)

Most Objects are Neutral Most objects we encounter in our daily lives are neutrally charged like couches, trees, and cows. When an object contains more protons than electrons it is described as positively charged, when an object contains more electrons than protons it is described as

negatively charged Most Objects are Neutral The reason big objects like couches, trees, and cows dont behave like charged particles is because they contain so many bazillions of protons and electrons that an extra few here or there wont really make much of a

difference. So even if they have a slight electric charge, it is too small, relatively speaking, to detect Tiny objects Tiny objects, like atoms, more commonly carry a measurable electric charge because they have so few protons and electrons that an

extra would make a big difference. Yes, you can still have large charged objects. Large charged objects For instance, when you walk across a carpeted floor in the winter, you pick up lots of extra charges and become a charged object yourself until you touch a doorknob

Then all the excess charge in your body travels through your finger and into the doorknob, causing you to feel a mild electric shock. Electric Charges Follow a simple rule: Like charges repel Opposite charges attract

Two positively charged particles will try to get as far away from each other as possible, while a positively charged particles and a negatively charged particle will try to get as close as possible. Types of Charges

Only two types of charges exist: Positive Negative If a question on the AP exam implies to give evidence of a third type of charge, reject that evidence! If a question on the AP exam suggests a kind of

charge that repels both positive and negative charges, reject that too! Coulombs Law So, just how much do charged objects attract and repel? Coulombs Law tells us! The closer two charges are to each other the stronger the force between them.

FACT: Coulombs Law is an equation for the force exerted by one electrical charge on another Coulombs Law Contd. The qs represent the amount of charge on each object The d represents the distance between the

two objects Variable k is the Coulombs law constant AP Type Question You will not be asked to calculate much with Coulombs law but the questions will be qualitative and semiquantitative. Example 1, if the amount of charge A is

doubled, what happens to the force of charge A on charge B? Example 2, if you double the distance between two charges, what happens to the force of one on the other? Conservation of Charge FACT: The total amount of charge in a system

(or in the universe itself) is always the same. Equal amounts of positive and negative charge can cancel out to make an object neutral, but those charges still exist on the object in the form of protons and electrons Conservation of Charge Charges can be transferred from one object to

another example by touching two charged metal spheres example scuffing your feed on the carpet BUT the total amount of charge stays the same. Circuits

A circuit is a wire path that allows charge to flow. A current is defined as the flow of positive charge Under what conditions would this charge flow through a wire? Circuits

It occurs when a coulomb of charge has a potential energy thats higher at one position in the wire than the other. We call this difference in potential energy per coulomb a voltage and a batterys job is to provide this voltage that allows current to flow. Current flows out of a battery from the positive

side of the battery to the negative Resistance Vs. Resistivity Resistance tells how difficult it is for charge to flow through something. Usually that something is a resistor, or a light bulb, or something that has a known or

determinable resistance Usually the resistance of the wires connecting the somethings together is nothing, at least compared to the resistance of the things. Resistance Vs. Resistivity FACT: The resistance R of a wire of known dimensions is given by

Resistance Vs. Resistivity The longer the wire is, the more its resistance The wider the wire is the less its resistance That is the bigger its cross-sectional area Two wires with the same shapes can have different resistances if they are made of different

materials Assuming the same shape, the wire with more resistance has a greater resistivity, represented by the variable ) is a property of a material, Circuits Circuit diagram: contains a battery and three

identical 100 ) resistors. What will AP ask? Questions about circuits will occasionally ask for calculation: Find the voltage across each resistor. Find the current through each resistor.

More often youll be asked qualitative questions Which bulb takes the greatest current? Rank resistors from largest to smallest voltage across. 4 Facts about Circuits FACT 1: Series resistors each carry the same

current, which is equal to the total current through the series combination. FACT 2: The voltage across series resistors is different for each but adds to the total voltage across the series combination. 4 Facts about Circuits

FACT 3: The voltage across parallel resistors is the same for each and equal to the total voltage across the parallel combination FACT 4: Parallel resistors each carry different currents, which add to the total current through the parallel combination.

AP Exam Tip If you are confused by a qualitative circuit question, try answering with a calculation: Well, with a 150-V battery heres a calculation showing that I get 1 A of current in the circuit, but with a 75-V battery I only get 0.5 A. Thus, cutting the batterys voltage in half also cuts the current in half.

V-I-R chart When you see a circuit, regardless of what questions about it are asked, its worth making a V-I-R chart listing the voltage, current, and resistance for each resistor. Then the 4 facts about circuits and Ohms Law V = IR can be used to find the missing value

on any row of the chart. V-I-R chart Start by sketching a chart and filling in known values. Right now, we know the resistance of each resistor. The voltage of the battery is 100 V.

V-I-R chart V-I-R chart Simplify the circuit, collapsing sets of parallel and series resistors into their equivalent resistors.

Equivalent Resistors FACT: The equivalent resistance of series resistors is the sum of all of the individual resistors. The equivalent resistance of parallel resistors is less than any individual resistor. Equivalent Resistors You can use this equation to find the

equivalent resistance of resistors that are in parallel: Here, then, the parallel combination of resistors has equivalent resistance of 50 ). Equivalent Resistors You can use this equation to find the

equivalent resistance of resistors that are in series: Since the other 100 ) resistor is in series with the 50 ) equivalent resistance, the equivalent resistance of the whole circuit is 150 ). V-I-R Chart

Now we can add this information into the chart. MISTAKE! The V-I-R Chart is not a magic square, its a tool for organizing your calculations for a complicated circuit. You can NOT just add values up and down the

columns. Ohms Law Now that we have made progress and two of the three entries in the total row are complete. Therefore, we can use Ohms Law to calculate the total current in this circuit.

Ohms Law FACT: Ohms law says that voltage across a circuit element equals that elements current times its resistance. V-I-R Chart & Ohms Law This equation can ONLY be used across a

SINGLE row in a V-I-R chart. In the total row, (100V) = I * (150 )) Therefore the current I=0.67 A. What do we use? Now we cant use Ohms law because we dont have any rows missing just one entry so we have to go back to our 4 Key Facts!

Using the Facts Resistor R1 is in series with the battery; since current through series resistors is equal to the total current, R1 must take the entire current flowing from the battery, all 0.67 A. AHA! Now you can put 0.67 A in the chart for the current through R1, and we can use Ohms

Law to calculate the voltage across R1; thats 67 V. V-I-R Chart Circuit Contd. Now to figure out R2 and R3. Look at their 50 ) equivalent resistor in the redrawn diagram.

Its in series with the 100 ) resistor. Therefore, the 50 ) resistor must add its voltage to 67 V to get the total voltage of 100 V and the voltage across the 50 ) equivalent resistor is 33 V. Facts again! Parallel resistors take the same voltage across

each that is equal to the total voltage across the combination. Both R2 and R3 take 33 V across them. V-I-R Chart Ohms Law again Now use Ohms Law across the rows for R2 and

R3 to finish the chart. (33 V) = I * (100 )) The current will be 0.33 A. V-I-R Chart V-I-R Chart Now the chart can be used to answer any

qualitative question. Yes, you need to give more justification then hey, look at my chart! The chart will ensure you get the right answers, and that you have a clue about how to approach the qualitative questions. AP Type Question

Example, the exam might ask the following: Rank the voltage across each resistor from largest to smallest. Justify your answer. Kirchoffs Law: Conservation of Charge and Energy FACT: Kirchoffs junction rule says that the

current entering a wire junction equals the current leaving the junction. This fact is a statement of conservation of charge: Since charge cant be created or destroyed, if 1 C of charge enters each seconds, the same amount each second must leave.

Kirchoffs Law: Conservation of Charge and Energy FACT: Kirchoffs loop rule says that the sum of voltage changes around a circuit loop is zero. This fact is a statement of conservation of energy because voltage is a change in the electrical potential energy of 1 C of charge. A battery can raise the electrical potential energy

of some charge that flows; a resistor will lower the potential energy of that charge. But the sum of all these energy changes must be zero. Kirchoffs Laws and 4 Key Facts Looking back at the Four Key Facts: These are just restatements of Kirchoffs Laws and thus of conservation of energy and charge.

Junction Rule The junction rule applies to the facts about current. Series resistors take the same current through each, because theres no junction. The current through parallel resistors adds to the total because of the junction before and

after the parallel combination. Junction Rule Conservation of charge Loop Rule The loop rule applies to the facts about

voltage. The voltage across series resistors adds to the total voltage because the resistors can only drop the potential energy of 1 C of charge as much as the battery raised the charges potential energy. Loop Rule

The voltage across parallel resistors must be the same because Kirchoffs loop rule applies to all loops of the circuit. No matter which parallel path you look at, the sum of the voltage changes must still be zero. Loop Rule Conservation of energy

Power in a Circuit Power is defined as energy per second. Resistors generally convert electrical energy to other forms of energy The amount of power says how quickly that conversion occurs

Power in a Circuit To determine the power dissipated by a resistor, use the equation P= IV However, using Ohms Law you can show that IV is equivalent to I2R as well as V2/R AP Exam Tip If the AP exam asks about power, or

equivalently the energy dissipated by a resistor per unit time make a fourth column on your V-I-R chart. Use whichever power equation you can and solve for power. Power Power doesnt obey the Four Key Facts. The total power dissipated by a bunch of

resistors is just the sum of the power dissipated by each, whether the resistors are in series, or parallel, or whatever. Circuits: Experimental Point of View When a real circuit is set up in the laboratory, it usually consists of more than just resistors

light bulbs and motors are common devices to hook to a battery. For the purposes of computation, though, we can consider pretty much any electronic device to act like a resistor. Circuits: Experimental Point of View

But what if your purpose is NOT computation? Often on the AP Exam, as in the laboratory, you are asked about observational and measurable effects. The most common questions involve the brightness of light bulbs and the measurement (not just computation) of current and voltage.

Brightness of a Bulb The brightness of a bulb depends solely on the power dissipated by the bulb. Remember the power equations The bulbs power can change depending on the current and voltage its hooked up to

Question A light bulb is rated at 100 W in the United States, where the standard wall outlet voltage is 120 V. If this bulb were plugged in in Europe, where the standard wall outlet voltage is 240 V, which of the following would be true? A) The bulb would be one-quarter as bright B) The bulb would be one-half as bright

C) The bulbs brightness would be the same D) The bulb would be twice as bright E) The bulb would be four times as bright Temperature Under most operating conditions, the resistance of the lightbulb is a property of the bulb itself, and so it will not change much no matter to

what the bulb is hooked. That said, the resistance of a bulb can vary when the bulbs temperature is very cold or very hot. You can assume a bulb has constant resistance unless a problem clearly asks you to consider temperature variation. Ammeters and Voltmeters

Ammeters measure current, and voltmeters measure voltage. This is pretty obvious, because current is measured in amps, voltage in volts. It is NOT necessarily obvious, though, how to connect these meters into a circuit. Ammeters and Voltmeters

Remind yourself of the properties of series and parallel resistors Voltage is the same for any resistors in parallel with each other So if youre going to measure the voltage across a resistor, you must put the voltmeter in parallel with the resistor.

Ammeters and Voltmeters Ammeters and Voltmeters In the picture, the meter labeled V2 measures the voltage across the 100 ) resistor, while the meter labeled V1 measures the potential difference between points A and B (which is also the voltage across R1).

Ammeters and Voltmeters Current is the same for any resistors in series with one another So, if youre going to measure the current through a resistor, the ammeter must be in series with that resistor

Ammeters and Voltmeters Ammeters and Voltmeters Ammeter A1 measures the current through resistor R1, while ammeter A2 measures the current through resistor R2. Is there a way to figure out the current in the other three resistors based on the readings in

these two ammeters?

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