Electric Circuits Notes 1 – Circuits

Voltage (V): The units of voltage are __________________ ( ) Resistance (R): The units of resistance are __________________ ( )

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.

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 _________________________ _________________!!!

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 ____________ ( ).

These three quantities are related using Ohm’s Law:

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.

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?

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 heater emits 1.00x102 W when connected to a 120 V power line. What is the resistance in the heater?

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.

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:

Kirchhoff’s Current Law For a series circuit: In a series circuit there is only one path so the current must be… For a parallel circuit: In a parallel circuit the charge can take different paths. Therefore the amount of charge at any point… Kirchhoff’s Current Law can be directly stated as: the sum of currents entering a junction…

IT =

IT =

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: Since there is only one path, the total voltage increase across the battery must equal the total drop across each resistor.

VT =

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: 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.

VT =

RT =

For a parallel circuit: 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.

RT =

For a parallel circuit: Note that the potential difference is…

Let’s recap:

Formula Series Parallel

Example: What are the values of I1, I2 and I3 in the circuit shown? Example: What is the value of R2 in the circuit shown?

Example: What is the potential difference supplied by the power source in this circuit? What are the values of V1, V2 and R2 in the circuit?

Electric Circuits Notes 4 – Electromotive Force

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 _______. When a battery goes dead it is because…

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.

Example: If a 12.0 V battery has an internal resistance of 0.220 ohms, what is the terminal voltage of the battery when a current of 3.00 A flows through the battery?

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… In fact 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?

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. (3.44x1020

)

2) How long would it take 2.0x1020

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?

(21 800 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? (7.5x1021

)

10) A student designed an experiment in order to measure the current through a resistor at different voltages.

Given the following data:

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)

Voltage (V) Current (I)

3.0 0.151

6.0 0.310

9.0 0.448

12.0 0.511

15.0 0.750

Worksheet 7.2

1) What are the values of the currents shown?

(2 A, 2 A, 2A)

2) Find the value of R2.

(12 Ω)

3) What is the potential difference supplied by the power source?

(36 V)

4) Find the values of V1, V2 and R2.

(40 V, 40V, 12 Ω)

5) Find the value of I3.

(3.6 A)

6) Find the value of V2.

(4 V)

7) Find the value of V2 and V3.

(34 V, 34 V)

8) What is the total resistance in this circuit?

(35 Ω)

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 I1, I2 and P1 in the following circuit?

(1.2 A, 1.2 A, 14.4 W)

13) What is the value of the total current in this circuit and the power dissipated by R1?

(7.5 A, 38W)

14) Find the values of the total current and I2 as well as the total power used by the circuit.

(3.5 A, 1.5 A, 42 W)

15) What are the values of I1, I2 and I3?

(2.7 A, 0.91 A, 2.7 A)

16) Find the potential difference of the power supply and the total power dissipated by the circuit below.

(60 V, 480 W)

17) Find the value of I1 and the total power used by the circuit.

(5.6 A, 140 W)

18) Find R3, I2, I3 and I4.

(16.7 Ω, 1.0 A, 3.0 A, 2.0 A)

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?

(7.95 V)

5) What is the terminal voltage of the battery in the circuit shown?

(10.9 V)

6) What is the EMF of the following battery?

(18 V)

7) Determine the internal resistance and the power dissipated by the internal resistance of the battery shown.

(3 Ω, 4.3 W)

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

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. 0.13 A c. 0.93 W 6. a. 16 V b. 180 W

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 0.050 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 0.0833 Ω in this circuit?

5) What is the internal resistance of the battery shown here?

6) A dry cell with an emf of 1.50 V and an internal resistance of 0.050 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 12.50 V. When a current of 35 A is drawn from it, its terminal voltage is 11.45 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. 2000 Ω c. 314 Ω 2. a. 10.0 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)