Electric Circuits Notes 1 Circuits

Transcription

1 Electric Circuits Notes 1 Circuits In the last chapter we examined how static electric charges interact with one another. These fixed electrical charges are not the same as the electricity that we use in everyday life, current electricity. Current electricity is all about The number of charges flowing per second is defined by the specific quantity current. Current (I): The unit of current is or ( ). However, current will not flow through a conductor unless there is (1) a potential difference ( ). (2) a. Some examples of voltage sources that we use everyday are: and. Consider a river. The rate of water flowing down the river is its current. Note that we talk about the rate of water flowing, not the speed that the individual water molecules are moving. The same is true for electric circuits, where the current represents how many electrons pass a certain point in a certain amount of time. Voltage (V): The units of voltage are ( ) These three quantities are related using Ohm s Law: Resistance (R): The units of resistance are ( ) Electric Current Consider a circuit of a battery connected to a light bulb. Which direction does the current flow? Unfortunately, there are two ways to consider this. 1) Electron Flow: The direction that the electrons actually move. The electrons go from the to the. 2) Conventional Current: Flow of positive charge. Positive charges flow from the to the. Although a little confusing (and more than a little irritating) we need to recall that electric potential is defined in terms of moving positive charge. And the direction of an electric field is defined as the direction that a positive charge will move in that field. In this class, unless otherwise stated, we will always use!!!

2 Power We often talk about the amount of power used by different electrical devices. This is often confused with voltage or energy. Recall that power is From the definition of power and Ohm s Law we can derive some formulae to describe electric power. P = W = ΔE and Ep = ΔVq t t Example: An electric fan has a resistance of 12 Ω and requires 0.75 A of current to function properly. What voltage is required to operate the fan? Example: An electric heater emits 1.00x10 2 W when connected to a 120 V power line. What is the resistance in the heater? To draw the various devices that can make up electric circuits, we use on schematic diagrams that are Schematic Name Function There are two ways that we can attach devices to a circuit. (1) Series: Ex. Draw a battery of two cells connected to two resistors in series. (2) Parallel: Ex. Draw a battery of two cells connected to two resistors in parallel.

3 Measuring Voltage and Current We can measure the voltage in a circuit using a and the current in a circuit using a. We need to connect these two devices in different ways. A voltmeter must be connected in. This is because a voltmeter measures the voltage drop a device. Ex. An ammeter must be connected in. This is because an ammeter measures the current a circuit. Ex. One last note There are two types of current. DC ( ) means it flows in one direction such as the current from a. AC ( ) means that it alternates the direction of flow. In the case of home electric circuits, they alternate at 60 Hz. As fun as it sounds AC is a little advanced for us just yet so we will be sticking to DC in this course.

4 Electric Circuits Notes 3 Kirchhoff s Laws We have already seen that we can connect devices to a circuit in two ways: or. The manner in which we attach components of a circuit can greatly affect the nature of the circuit in particular its there are a number of laws that we must use called: For a series circuit: Kirchhoff s Current Law In a series circuit there is only one path so the current must be I T = For a parallel circuit: In a parallel circuit the charge can take different paths. Therefore the amount of charge at any point I T = Kirchhoff s Current Law can be directly stated as: the sum of currents entering a junction Kirchhoff s Voltage Law Kirchhoff s Voltage Law is stated as: The sum of the potential differences in a circuit must In a way this is simply restating the Remember that there is an increase in the potential across the of a and that there is a decrease in potential across a. Essentially these increases and drops must add up to zero. For a series circuit: V T = Since there is only one path, the total voltage increase across the battery must equal the total drop across each resistor.

5 For a parallel circuit: V T = Note that the potential difference is Kirchhoff vs Ohm Kirchhoff does not have a law for resistance. However we can perform an arduous derivation to find the formula using Kirchhoff s other law and Ohm s Law. Instead, let s just reason it out. For a series circuit: R T = The total resistance in a series circuit is the of the. Since each electron must push its way through each resistor, it should make sense that the resistances are cumulative. For a parallel circuit: R T = We already know that as we add resistors in parallel, the total resistance If our marching soldiers are forced through one path, then there will be much more friction than if there are multiple paths to choose from. This is true even if the additional pathways are of higher resistance.

6 Let s recap: Formula Series Parallel Example: What are the values of I 1, I 2 and I 3 in the circuit shown? Example: What is the value of R 2 in the circuit shown?

7 Example: What is the potential difference supplied by the power source in this circuit? What are the values of V 1, V 2 and R 2 in the circuit?

8 Electric Circuits Notes 4 Electromotive Force We know that a battery is a source of potential difference ( ) or electric energy. When not connected to a circuit there is a potential difference between the terminals. This voltage is also known as Despite the name, this is a not a. This dates back to a time when we thought that the two were equivalent. For example a car battery has an EMF of and lithium battery has an EMF of. However, as soon as a battery is connected to a circuit and current flows through it the potential difference across the terminals is always This is due to the fact that every battery has Because of this the terminal voltage is always than the EMF of the battery. Where: Note: Ir = Note: If the battery is not connected to a circuit Consider the following diagram showing a circuit with an external resistance,, internal resistance and EMF. Example: If a 12.0 V battery has an internal resistance of ohms, what is the terminal voltage of the battery when a current of 3.00 A flows through the battery? When a battery goes dead it is because When a rechargeable battery is being charged an external voltage is applied to the battery. In order to force electrons backwards into the battery the external voltage must be Example: A 12.0 V car battery is being charged by an alternator that can supply 15 V. If the internal resistance of the battery is 1.3 ohms, what is the current through the battery? In fact the external voltage must be:

9 Worksheet 7.1 1) A current of 3.60 A flows for 15.3 s through a conductor. Calculate the number of electrons that pass through a point in the conductor in this time. (3.44x10 20 ) 2) How long would it take 2.0x10 20 electrons to pass through a point in a conductor if the current was 10.0 A? (3.2 s) 3) Calculate the current if a charge of 5.60 C passes through a point in a conductor in 15.4 s. (0.364 A) 4) What is the potential difference across a conductor to produce a current of 8.00 A if there is a resistance in the conductor of 12.0 Ω? (96 V) 5) What is the heat produced in a conductor in 25.0 s if there is a current of 11.0 A and a resistance of 7.20 Ω? ( J) 6) 150 J of heat are produced in a conductor in 5.50 s. If the current through the conductor is 10.0 A, what is the resistance of the conductor? (0.273 Ω) 7) What is the current through a 400 W electric appliance when it is connected to a 120 V power line? (3.33 A) 8) a. When an electric appliance is connected to a 120 V power line, there is a current through the appliance of 18.3 A. What is its resistance? (6.56 Ω) b. What is the average amount of energy given to each electron by the power line? (1.92x10-17 J) 9) a. What potential difference is required across an electrical appliance to produce a current of 20.0 A when there is a resistance of 6.00 Ω? (120 V) b. How many electrons pass through the appliance every minute? (7.5x10 21 ) 10) A student designed an experiment in order to measure the current through a resistor at different voltages. Given the following data: Voltage (V) Current (I) a. Draw a graph showing the relationship between current and voltage (V vs. I) b) Using the graph, what is the resistance of the resistor? (20.0 +/- 0.5 Ω)

10 Worksheet 7.2 1) What are the values of the currents shown? (2 A, 2 A, 2A) 2) Find the value of R 2. (12 Ω) 3) What is the potential difference supplied by the power source? (36 V) 4) Find the values of V 1, V 2 and R 2. (40 V, 40V, 12 Ω)

11 5) Find the value of I 3. (3.6 A) 6) Find the value of V 2. (4 V) 7) Find the value of V 2 and V 3. (34 V, 34 V) 8) What is the total resistance in this circuit? (35 Ω)

12 9) What is the total resistance in this circuit? (3.4 Ω) 10) What is the total resistance of this circuit? (4 Ω) 11) What is the total resistance of three resistors in parallel if their individual resistances are: 2 Ω, 4 Ω, and 8 Ω? (1.1 Ω) 12) What are the values of I 1, I 2 and P 1 in the following circuit? (1.2 A, 1.2 A, 14.4 W)

13 13) What is the value of the total current in this circuit and the power dissipated by R 1? (7.5 A, 38W) 14) Find the values of the total current and I 2 as well as the total power used by the circuit. (3.5 A, 1.5 A, 42 W) 15) What are the values of I 1, I 2 and I 3? (2.7 A, 0.91 A, 2.7 A)

14 16) Find the potential difference of the power supply and the total power dissipated by the circuit below. 17) Find the value of I 1 and the total power used by the circuit. (60 V, 480 W) 18) Find R 3, I 2, I 3 and I 4. (5.6 A, 140 W) (16.7 Ω, 1.0 A, 3.0 A, 2.0 A)

15 Worksheet 7.3 1) A battery in a remote control has an EMF of 1.5 V and an internal resistance of 0.3 Ω. If there is a current of 0.5 A running through the circuit, what is the terminal voltage of the battery? (1.35 V) 2) What is the EMF of a battery that has an internal resistance of 0.8 Ω and a terminal voltage of 10 V when a current of 2.4 A runs through it? (11.9 V) 3) A battery has an EMF of 9.0 V and an internal resistance of 0.50 Ω. What is the terminal voltage when it is connected to a circuit with a resistance of 4.0 Ω? (8.0 V) 4) What is the terminal voltage of the battery in the circuit shown? 5) What is the terminal voltage of the battery in the circuit shown? (7.95 V) 6) What is the EMF of the following battery? (10.9 V) 7) Determine the internal resistance and the power dissipated by the internal resistance of the battery shown. (18 V) (3 Ω, 4.3 W)

16 Worksheet 7.2 Series and Parallel Circuits Determining Voltage, Current and Resistance

17 1) The current through A is 0.50 A when the switch S is open. What will the current be through A when the switch S is closed? 2) Which one of the following arrangements of four identical resistors will have the least resistance? 3) What is the current in the ammeter A in this circuit? 4) What is the voltage V of the power supply in the circuit below? 5) Use this circuit diagram to answer the questions below. a. What is the equivalent resistance of this circuit? b. What is the current through the 54 Ω resistor? c. How much power is dissipated in the 54 Ω resistor? 6) Use this circuit diagram to answer the questions below. a. What is the voltage across the 8.0 Ω resistor (between 1 and 2)? b. How much power is dissipated in the 5.0 Ω resistor? Answers: 1. (1.0 A) 2. (D) 3. (2.0 A) 4. (72 V) 5. a. 91 Ω b A c W 6. a. 16 V b. 180 W

18 Worksheet 7.4 EMF and Terminal Voltage 1) Calculate the equivalent resistance of each of the networks of resistors in the following circuits. 2) Use the circuit above to answer the following: a. What is the equivalent resistance of the circuit above? b. What is the voltage across the 6.0 Ω resistor? 3) A dry cell with an emf of 1.50 V has an internal resistance of Ω. What is the terminal voltage of the cell when it is connected to a 2.00 Ω resistor? 4) What is the emf of the battery if the current in A is 1.2 A and the internal resistance of the battery is Ω in this circuit? 5) What is the internal resistance of the battery shown here?

19 6) A dry cell with an emf of 1.50 V and an internal resistance of Ω Is shorted out with a piece of wire with a resistance of only 0.20 Ω. What will a voltmeter read if it is connected to the terminals of the dry cell at this time? 7) A battery has an emf of V. When a current of 35 A is drawn from it, its terminal voltage is V. What is the internal resistance of the battery? 8) A battery with an emf of 6.00 V has an internal resistance of 0.20 Ω. What current does the battery deliver when the terminal voltage reads only 5.00 V? 9) The in the diagram above is short-circuited with a wire of resistance 0.10 Ω. What is the terminal voltage under these conditions? Answers: 1. a. 7.0 Ω b Ω c. 314 Ω 2. a Ω b. 1.2 V 3. (1.46 V) 4. (10 V) 5. (0.50 Ω) 6. (1.20 V) 7. (0.030 Ω) 8. (5.0 A) 9. (0.25 V)