# Circuits. Circuits. Electric Current & DC Circuits. current and circuits presentation March 22, How to Use this File.

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2 Electric Current 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. I = ΔQ Δt 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. 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 off 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. Electric Current Electric Current The current, I = ΔQ Δt has the units Coulombs per second. The units can be rewritten as Amperes (A). Amperes are often called "amps". 1 A = 1 C/s 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. Electric Current 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. 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! 2

3 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. Circuits 1 12 C of charge passes a location in a circuit in 10 seconds. What is the current flowing past the point? 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. Mar 9 7:02 AM 2 A circuit has 3 A of current. How long does it take 45 C of charge to travel through the circuit? 3 A circuit has 2.5 A of current. How much charge travels through the circuit after 4s? Mar 9 9:39 AM Mar 9 9:39 AM 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. Batteries Click here for a Battery oltage Simulation from PhET Positive Terminal Negative Terminal 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 Mar 11 8:57 AM 3

5 6 What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 is applied across it? Electrical Power Power is defined as work per unit time P = W t if W = Q then substitute: if I = Q then substitute: t P = Q t P = I What happens if the current is increased? What happens if the voltage is decreased? Mar 12 9:02 AM Mar 11 9:20 AM Electrical Power 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. 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? Mar 11 10:28 AM Mar 11 10:28 AM Electrical Power Electrical Power How can we re write electrical power by using Ohm's Law? (electrical power) P = I P = R P = 2 R (Ohm's Law) I = R Is there yet another way to rewrite this? I = can be rewritten as = IR. R (electrical power) P = I (Ohm's Law) = I R We can substitute this into Power P = I(IR) P = I 2 R Mar 11 10:28 AM Mar 11 10:28 AM 5

6 Batteries D, C, AA, & AAA have the same voltage, however they differ in the amount of power they deliver. 7 A toy car's electric motor has a resistance of 17 Ω; find the power delivered to it by a 6 battery. D C AAA AA 9 For instance, D batteries can deliver more current and therefore more power. 1.5 Mar 11 10:34 AM 8 What is the power consumption of a flash light bulb that draws a current of 0.28 A when connected to a 6 battery? 9 A 30Ω toaster consumes 560 W of power: how much current is flowing through the toaster? Mar 11 10:44 AM Mar 11 10:45 AM 10 When 30 is applied across a resistor it generates 600 W of heat: what is the magnitude of its resistance? Resistivity and Resistance Return to Table of Contents Mar 12 9:26 AM resistivity and resistance 6

7 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... "Pipe" size if there were pipes with water in them, what could we do to the pipes to change the speed of the water (the current)? 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 (ρ). Combining what we know about A, L, and ρ, we can find a conductor's total resistance. R = ρ L A Mar 9 7:41 PM Mar 9 7:41 PM Resistivity & Resisitance Resistance, R, is measured in Ohms (Ω). Ω is the Greek letter Omega. Cross sectional area, A, is measured in m 2 Length, L, is measured in m R = ρ L A Resistivity, ρ, is measured in Ωm What is the resistance of a good conductor? Low; low resistance means that electric charges are free to move in a conductor. Click here for a PhET simulation about Resistance Resisitance ρ = RA L How can we define A for a wire? Mar 9 7:41 PM Mar 9 7:41 PM Resistivities of Common Conductors Material Resistivity (10 8 Ωm) Silver 1.59 Copper 1.68 Gold 2.44 Aluminum 2.65 Tungsten 5.60 Iron 9.71 Platinum 10.6 Mercury 98 Nichrome Rank the following materials in order of best conductor to worst conductor. A B C Iron, Copper, Platinum Platinum, Iron, Copper Copper, Iron, Platinum Material Silver Copper Gold Aluminum Tungsten Iron Platinum Mercury Nichrome Resistivity (10 8 Ωm) Mar 9 7:41 PM Mar 9 7:41 PM 7

8 12 What is the resistance of a 2 m long copper wire whose cross sectional area of 0.2 mm 2? 13 An aluminum wire with a length of 900 m and crosssectional area of 10 mm 2 has a resistance of 2.5 Ω. What is the resistivity of the wire? Mar 9 9:44 PM Mar 12 8:26 AM 14 What diameter of 100 m long copper wire would have a resistance of 0.10 Ω? 15 What is the length of a 10 Ω copper wire whose diameter is 3.2 mm? Mar 12 8:39 AM Mar 9 9:48 PM 16 The length of a copper wire is cut to half. By what factor does the resistance change? 17 The radius of a copper wire is doubled. By what factor does the resistivity change? A 1/4 B 1/2 C 2 D 4 A 1/4 B 1/2 C 1 D 2 Mar 9 9:48 PM Mar 9 9:48 PM 8

9 Circuit Diagrams Circuit Diagrams Grade:«grade» Subject:AP Physics 1 Date:«date» Return to Table of Contents Mar 9 3:48 PM circuit diagrams Circuit Diagrams Circuit Diagrams Drawing realistic pictures of circuits can be very difficult. For this reason, we have common symbols to represent each piece. Draw a simple circuit that has a 9 battery with a 3 Ω resistor across its terminals. What is the magnitude and direction of the current? Resistor Battery Wire *Note: Circuit diagrams do not show where each part is physically located. Conventional current flows from the positive terminal to the negative terminal. Circuit Diagrams There are two ways to add a second resistor to the circuit. Circuit Diagrams Are the following sets of resistors in series or parallel? Series Parallel All charges must move through both resistors to get to the negative terminal. Charges pass through either or but not both. 9

10 Equivalent Resistance Series Circuits: 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. What happens to the current in the circuit to the right? The process of reducing the resistors in a circuit is called finding the equivalent resistance (R eq ). Series Circuits: Equivalent Resistance Series Circuits: Equivalent Resistance If = substitute Ohm's Law solved for is: = IR What happens to the voltage as it moves around the circuit? IR = I 1 I 2 I 3 R 3 but since current (I) is the same everywhere in a series circuit, IR = I I IR 3 I = I 1 = I 2 = I 3 R eq = R 3... Now divide by I 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? 1 What is the equivalent resistance in this circuit? 2 What is the total current at any spot in the circuit? = 5Ω = 5Ω = 9 = 9 Mar 16 8:49 AM Mar 16 8:49 AM 10

11 3 What is the voltage drop across? 4 What is the voltage drop across? = 5Ω = 5Ω = 9 = 9 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. Mar 16 8:49 AM Mar 16 8:49 AM 5 How much power is used by? Parallel Circuits: Equivalent Resistance = 5Ω What happens to the current in the circuit to the right? = 9 Mar 16 8:49 AM Parallel Circuits: Equivalent Resistance Parallel Circuits: Equivalent Resistance If I = I 1 I 2 I 3 Rewrite Ohm's Law for I and substitute for each resistor What happens to the voltage as it moves around the circuit? R = R 3 Also, since = 1 = 2 = 3 so we can substitute for any other voltage R R = = ( 1 1 R = R eq R 3 1 R 3 ( oltage is a common factor, so factor it out! Divide by to eliminate voltage from the equation. If you add more resistors in parallel, what will happen the to resistance of the circuit? 11

12 6 What is the equivalent resistance in the circuit? 7 What is the voltage at any spot in the circuit? = 3Ω = 18 = 6Ω = 18 = 6Ω Mar 19 8:41 AM Mar 19 8:41 AM 8 What is the current through? 9 What is the current through? = 6Ω = 6Ω = 18 = 18 Mar 19 8:41 AM Mar 19 8:41 AM 10 What is the power used by? 11 What is the power used by? = 6Ω = 6Ω = 18 = 18 Mar 19 8:41 AM Mar 19 8:41 AM 12

13 12 What is the total current in this circuit? 13 What is the voltage drop across the third resistor? R 3 = 4Ω R 3 = 4Ω = 6Ω = 6Ω = 18 = 18 Mar 19 8:41 AM Mar 19 8:41 AM 14 What is the current though the first resistor? R 3 = 4Ω Kirchhoff's Rules = 6Ω = 18 Grade:«grade» Subject:AP Physics 1 Date:«date» Mar 19 8:41 AM Mar 9 3:49 PM oltmeter Measurement oltage is measured with a voltmeter. oltmeters are connected in parallel and measure the difference in potential between two points. Return to Table of Contents 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. Measurement 13

14 current and circuits presentation 2016 Ammeter Multimeter Although there are separate items to measure current and voltage, there are devices that can measure both (one at a time). Current is measured using an ammeter. These devices are called multimeters.multimeters can also measure resistance. Ammeters are placed in series with a circuit. In order to not interfere with the current, the ammeter has a very low resistance. Click here for a PhET simulation on circuits 1 A group of students prepare an experiment with electric circuits. Which of the following diagrams can be used to measure both current and voltage? L B C D EMF & Terminal oltage A Return to Table of Contents E Jul 20 9:27 PM EMF Electromotive Force Electromotive Force Req A battery is a source of voltage AND a resistor. Req r Terminal voltage (T) is the voltage measured when a voltmeter is across its terminals. Each battery has a source of electromotive force and internal resistance. E _ Electromotive force (EMF) is the process that carries charge from low to high voltage. r E _ If there is no circuit attached, no current flows, and the measurement will equal the EMF. If however a circuit is attached, the internal resistance will result in a voltage drop, and a smaller terminal voltage. (E Ir) Another way to think about it is that EMF is the voltage you measure when no resistance is connected to the circuit. 14

15 Terminal oltage 2 When the switch in the circuit below is open, the voltmeter reading is referred to as: R eq r E _ We say that the terminal voltage is: T = E Ir Maximum current will occur when there is zero external current. A EMF B Current C Power D Terminal oltage E Restivity When solving for equivalent resistance in a circuit, the internal resistance of the battery is considered a series resistor. R EQ = R int R ext Jul 20 9:31 PM 3 When the switch in the circuit below is closed, the voltmeter reading is referred to as: 4 A 6 battery, whose internal resistance 1.5 Ω is connected in series to a light bulb with a resistance of 6.8 Ω. What is the current in the circuit? A Terminal oltage B EMF C Current D Resistance E Power Jul 20 9:32 PM Mar 23 8:47 AM 5 A 6 battery, whose internal resistance 1.5Ω is connected in series to a light bulb with a resistance of 6.8Ω. What is the terminal voltage of the battery? 6 A 25 Ω resistor is connected across the terminals of 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? Mar 23 8:47 AM Mar 23 9:30 AM 15

16 Kirchhoff's Rules Kirchhoff's Rules 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. Return to Table of Contents Kirchhoff's Rules 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, I 1 I 2 = I 3 Kirchhoff's Rules I 3 I 1 I 2 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, Kirchhoff's Rules The sum of the voltage drops is equal to the voltage across the battery =0 OR = 1 2 Problem Solving with Kirchhoff's Rules 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.) Problem Solving with Kirchhoff's Rules Find the unknowns in the following circuit: I 2 = 2.6 A = 5Ω R 3 =? R 4 = 2Ω 3 = 1.87 = Solve the equations algebraically. 16

17 Problem Solving with Kirchhoff's Rules First, label and for each battery. I 2 = 2.6 A = 5Ω R 3 =? R 4 = 2Ω 3 = 1.87 _ = 12 Next, label the current in each branch with a symbol and an arrow. Problem Solving with Kirchhoff's Rules I 1 = 5Ω I 3 I 4 R 3 =? 3 = 1.87 R 4 = 2Ω = 12 I I 2 = 2.6 A _ Problem Solving with Kirchhoff's Rules Next, apply the junction rule to each junction. Problem Solving with Kirchhoff's Rules Next, apply the loop rule to each loop. I 1 I 2 = 2.6 A I 1 I 2 = 2.6 A = 5Ω I 3 I 4 R 3 =? 3 = 1.87 R 4 = 2Ω _ = 12 I = 5Ω I 3 I 4 R 3 =? 3 = 1.87 R 4 = 2Ω _ = 12 I I = I 3 I 4 I = I 2 I 1 = I 3 Problem Solving with Kirchhoff's Rules Problem Solving with Kirchhoff's Rules List the givens and use ohm's law to solve for the unknowns. Find the unknowns in the following circuit: R 3 = 2 Ω Current (Amps) oltage (olts) Resistance (Ohms) R R 4 2 Total 12 = 10? Ω I 1 = 7 A 1 = 70? = 23? Ω I 2 = 3 A 2 = 70? I 3 = 10 A 3 = 20? R 4 = 3 Ω I 4 = 10? A 4 = 30? I = I 3 I 4 I = I 2 I 1 = I 3 = = = 4 =

18 Mar 9 3:50 PM 18

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