CIRCUITS: Series & Parallel

Last Week s BIG IDEAS: Opposite charged objects attract Like charged objects repel

Last Week s BIG IDEAS: The electrons are the loose particles that move to make things charged not the protons. Protons are locked in more solid relationships in the nucleus and don t get around.

Last Week s BIG IDEAS: The attractive force between particles/objects depends on the amount of charge (in Coulombs) the objects have and the distance (in m) between the two particles/objects. The above relationship is called Coulomb s Law and is given by: F e = k q 1 q 2 r 2

Last Week s BIG IDEAS: Coulomb s Law of attraction: F e = k q 1 q 1 r 2 For the eensy-beensy particles like atoms, electrons, and protons Is a lot like Newton s Law of Universal Gravitation F g = G m 1 m 2 r 2 for the big particles like planets. The only difference is that Newton s Law is only attractive and Coulomb s Law can be both attractive and. repulsive

Last Week s BIG IDEAS: Planets behave like particles to some degree

Last Week s BIG IDEAS: Both Coulomb s Law of attraction - F e = k q 1 q 1 r 2 and Newton s Law of Universal Gravitation - F g = G m 1 m 2 r 2 are examples of forces at a distance (far away) where the objects are not touching and can be far away. These are different from contact forces such as friction, tension, force of push or pull in which the objects are in direct contact with each other.

Voltage (Electric Potential Difference), Current, and Resistance What is this illustration showing? What does voltage do? What does current (ampere) represent? And what does resistance do?

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) elastic Electric potential energy is like potential energy and gravitational potential energy Higher Potential Energy + GPE Lower Potential Energy - ELPE EPE

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) To cause movement of a charge, there must be an electric potential difference between two points in the electric circuit just as there could be a difference in water pressure between two points in a plumbing system.

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) In the image below, there is more electrical pressure at the 6 V side of the battery than the 0 V side. Imagine that the 6 V side is negatively (-) charged and so electrons are pushed away (like charges repel) through the circuit towards the side of the battery which is positively (+) charged to which the electrons are (opposite attracted charges attract). +

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) In this circuit the energetic electrons have two paths they can go through. In the middle of each path is something that is resisting the flow of electrons and thus they struggle to get through. In the struggle they some use up of their electrical energy which turns into light and heat energy. The electrons are moving slower after the work (in Joules) they have performed. DIRECTIONS: Use the right terms below in the blanks above WORD BANK resisting two heat Use up work +

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) Suppose there was a U. S. Navy nuclear submarine crew that just happened to be all guy sailors. They just got off their 3-month tour on their boat and are repelled from the sight of each other. They are seeking out members of the opposite and sex go down to the only two clubs on this small island they are docked at to party-hardy. Once they ve used up their energy they head back tired to their. submarine DIRECTIONS: Use the right terms below in the blanks above WORD BANK sex submarine used Navy repelled +

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) Potential energy Potential energy For example, to push a positively charged Styrofoam pellet into a positively charged electric field requires work (a force through a distance) The Styrofoam gains electrical potential energy in the process Since like charges, repel the charged Styrofoam moves away from the Van de Graaf generator converting its electrical potential energy into kinetic energy

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) DIRECTIONS: Put the correct term in the correct blank below. WORD BANK random section Prom speeds open In an electrical circuit, while the switch is : open Free electrons (conducting electrons) are always moving in random motion. speeds The random are at an order of 1,000,000 m/s. There is no net movement of charge across a cross section of a wire. It is all back and forth and random. Its like the random movement of single kids dancing at. Prom

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) closed What occurs in a wire when the circuit switch is? An electric field is established instantaneously (at almost the speed of, light 3x10 8 m/s). Free electrons, while still randomly moving, immediately begin drifting due to the electric field, resulting in a net flow of charge. They are like users who think have free will but are in fact being manipulated to move in certain directions. Average drift velocity is about 0.01cm/s. The effect of the manipulation on FB users is small but since there are billions of them, like electrons, the overall effect is large. WORD BANK users closed light free billions

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) What occurs in a wire when the circuit switch is closed and electricity begins to flow? Much like a group of students going to the bus circle after school, they slowly drift out at school in a messy but deliberate pattern. The electric field is kind of like monitors hall telling students to go home and get out of the building. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/micohm.gif

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) The electric potential V (or voltage) is the potential for creating electric potential energy if a charge is placed at a given point. It is defined as the energy per unit charge: V = U elec q Where U elec is the electric potential energy (in Joules) and q is the charge of an object in Coulombs. 1 volt = 1 V = 1 Joule per Coulomb, = 1 J/C An electric field exerts an electrical force F E on a charge q. An electric potential V tells how much electrical energy U elec each charge q has.

VOLTAGE (ELECTRIC POTENTIAL DIFFERENCE) Another definition. Voltage: Electrical pressure that pushes charges along a conducting pathway. Metric Unit for Voltage: Volt (V)

high Electric Charges always travel from a electrical pressure region to a pressure region. low

1 AMPERE of current carries about electrons per second CURRENT Electric Current: The flow of electrons through a conducting electrons pathway. It relates to how many pass a given place in a wire in one second. Metric Unit for Current: 1 ampere (A) = 6.24 x 10 18 e - /s

RESISTANCE resist Resistance: The tendency of a substance to the flow of e - s. Metric Unit: The force opposing e - movement is measured in Ohms (Ω).

RESISTANCE All materials have some resistance, insulators have a large amount of resistance, while conductors have very little resistance. As e-s flow through material and collide with atoms, electrical energy is converted into two forms of energy: and. heat light

RESISTANCE The electricity has two paths to flow through. The 10 Ohm resistor allows three times as many electrons/ions to flow as the 30 Ohm resistor.

RESISTANCE Variable resistor The knob turning is applying variable resistance to the circuit. This can be seen because the - light level of the LED is fluctuating. The variable resistor is controlling the number of electrons (e - s) passing through the circuit, or, in other words, the current (in Amps).

CURRENT, VOLTAGE, & RESISTANCE Make an analogy for voltage, resistance, and current like the ones below

Electrical Circuits

Circuit Symbols: Battery Resistor Light-bulb Switch Wire DIRECTIONS: Draw lines from each term to the corresponding item in the circuit diagram at right

Three general types of circuits: DIRECTIONS: Put the correct term in the correct blank below. WORD BANK Power source Short resistance Closed current Open Closed Circuit - There is a complete loop with wires going from one side of the power source through a resistor(s) to the other side of the. Open Circuit - There is not a complete loop for to flow. Short Circuit - There is a complete loop, but it does not contain any to the flow of electricity.

Three general types of circuits: Closed Circuit - There is a complete loop with wires going from one side of the power source through a resistor(s) to the other side of the. Open Circuit - There is not a complete loop for to flow. Short Circuit - There is a complete loop, but it does not contain any to the flow of electricity. Only Working Circuit WORD BANK Power source Short resistance Closed current Open

There are two ways to put resistors into a circuit. 1. Resistors can be in series OR 2. Resistors can be in parallel

Resistors in Series Resistors are considered to be in series if the current must go through all of the resistors in order. The current (amps) through all resistors in series is the same. The voltage across resistors in series may be different The rate of electron flow (or current) is determined by which resistor? Ans. The resistor with the largest amount of ohms. R 1 R 2 R 3

Combining (adding) Resistors Series Resistors R 1 To find the total current just add up the currents through each resistor: I total = I 1 = I 2 = I 3 R 2 To find the total resistance, just add up the resistances of each resistor: R eq = R total = R 1 + R 2 + R 3 R 3 Voltage is calculated with Ohm s Law Amps I = V R Q

Resistors in Parallel Resistors are considered to be in parallel if the current is shared between multiple resistors. The current (amps) through all resistors in parallel may be different. The voltage across all parallel resistors is the same. Will a resistor with a large resistance have more or less current through it then a resistor with a small resistance? Ans. The resistor with a large resistance will have a smaller current then the resistor with the smaller resistance. R 1 R 2 R 3

Combining (adding) Resistors Parallel Resistors Current is calculated with Ohm s Law: I = V R R 1 R 2 R 3 Total resistance: 1 1 1 = + + R R R total 1 V total = V 1 = V 2 = V 3 2 1 R 3

Example 1: A circuit has three resistors - an 8.0 W, 5.0 W and a 12 W resistor - in series along with a 24 V battery. Draw the circuit. Calculate the total resistance of the circuit. Calculate the total current through the circuit. What is the current through each resistor? Calculate the voltage across each resistor.

P.O.D. 1: A circuit has three resistors - a 6.0 W, a 4.0 W and a 9 W resistor - in series along with a 36 V battery. Draw the circuit. Calculate the total resistance of the circuit. Calculate the total current through the circuit. What is the current through each resistor? Calculate the voltage across each resistor.

Example 2: A circuit has three resistors: 6.0 W, 4.0 W and a 12 W resistors in parallel along with a 24 V battery. Draw the circuit. Calculate the total resistance of the circuit. Calculate the total current through the circuit. What is the voltage across each resistor? Calculate the current across each resistor.

P.O.D. 2: A circuit has three resistors: 4.0 W, 6.0 W and a 8 W resistors in parallel along with a 30 V battery. Draw the circuit. Calculate the total resistance of the circuit. Calculate the total current through the circuit. What is the voltage across each resistor? Calculate the current across each resistor.

Electrical Outlets Electrical outlets provide electric potential (or the voltage) for any appliance plugged in to it. In the United States ALL outlets provide 120 V (in Europe it is 240 V)

Example 3: What will the current be if an American-made 55 W light bulb is plugged in to a 220 V power source? We have worked with Power before in our Energy Unit. It is measured in Watts It was given by the formula P = W t For electricity we have three alternative shortcut formulas for Power based on what is given in the problem: P = I 2 R, P = I V, P = V2 For this problem we use which one? P = I V Solving for I I = P V SOLUTION: I = P 55 W = =0.25 Amps V 220 V R

P.O.D. 3: What will the resistance be if a European-made 55 W light bulb is plugged in to a 210 V power source? What about an American-made 55 W light bulb?

MULTIPLE CHOICE: As more identical resistors R are added to the parallel circuit shown, the total resistance between points P and Q R 1. Increases 2. Remains the same 3. Decreases P Q

MULTIPLE CHOICE: As more identical resistors R are added to the parallel circuit shown, the total resistance between points P and Q 1. Increases 2. Remains the same 3. decreases R P Q Q

MULTIPLE CHOICE: When one bulb is unscrewed, the other bulb will remain lit in which circuit 1. I 2. II 3. Both 4. Neither Circuit II Circuit I

MULTIPLE CHOICE: When one bulb is unscrewed, the other bulb will remain lit in which circuit 1. I 2. II 3. both 4. neither Circuit I Circuit II

EXAMPLE 4: A 25W bulb and a 100W bulb are connected in series. Which bulb will glow brighter?

25W 100W 120V

The Light Bulbs are really Resistors A) Calculate the resistance for each resistor shown. B) Calculate the total resistance of the circuit. C) Calculate the current through each resistor. D) Calculate the power used by each resistor. E) Calculate the voltage across each resistor. 25W 100W 120V

25W Bulb Part A. 100W Bulb V P = R 2 V R = P 2 120 2 R = 25 R = 576W P = V2 R is the formula for electrical Power. Another formula for Power is P = I V R = 120 2 100 R = 144W

B) The total resistance (R total ) 25W 576 W 100W 144 W 120V + = 576 W + 144 W = 720 W

C) Calculate the total circuit current (I) 720 W 120V The current in a series circuit is the same throughout Use Ohm s Law: I = V R 120V = 720 W = 0.17amps

D) Calculate the Power used by each resistor. 576 W 144 W 25 W Bulb 100 W Bulb 120V P 1 = 25 W P 2 = 100 W

E) Calculate the Voltage across each resistor. 576 W 144 W =.167 amps 120V 25W Bulb 100W Bulb Use Ohm s Law: V = I R = (0.167 amps)(576 W) = 96.2 V Use Ohm s Law: V = I R = (0.167 amps)(144 W) = 24 V

P.O.D. 4: B) Calculate the total resistance of the circuit. A) Calculate the total current in the circuit. C) Calculate the current through each resistor. D) Calculate the power used by each resistor. E) Calculate the voltage across each resistor. 200 W 300 W 120V

The circuit below consists of two identical light bulbs burning with equal brightness and a single 12V battery. When the switch is closed, the brightness of bulb A A 1. Increases 2. Decreases 3. Remains unchanged

The circuit below consists of two identical light bulbs burning with equal brightness and a single 12V battery. When the switch is closed, the brightness of bulb A 1. Increases 2. decreases 3. remains unchanged When the switch is closed, bulb B goes out because all of the current goes through the wire parallel to the bulb. Thus, the total resistance of the circuit decreases, the current through bulb increases, and it burns brighter. A Q

Which bird is in trouble when the switch is closed? 1) Bird 1 2) Bird 2 3) Neither 4) Both 1 2

Which bird is in trouble when the switch is closed? 1) Bird 1 2) bird 2 3) neither 4) both 1 2

Charge flows through a light bulb. Suppose a wire is connected across the bulb as shown. When the wire is connected 1. All the charge continues to flow through the bulb, and the bulb stays lit. 2. Half the charge flows through the wire, the other half continues through the bulb. 3. Essentially all the charge flows through the wire and the bulb goes out. 4. None of these. Q

EXAMPLE: Analyze the circuit: A) Calculate R total B) Calculate the current through each resistor. C) Calculate the voltage through each resistor. 8 W 60V 8 W 16 W 4 W

EXAMPLE: Analyze the circuit: A) Calculate R total B) Calculate the current through each resistor. C) Calculate the voltage through each resistor. Use the formula for resistors in Parallel: 1 R R 120V 1 2 R total 1 123 3 = = = 1 R 32 4 1 1 16 = + + 1 R 8W 2 1 32 + + 1 R 3 1 32 = 4 32 16W 16W 32W 32W

EXAMPLE: Analyze the circuit: A) Calculate R total B) Calculate the current through each resistor. C) Calculate the voltage through each resistor. 16W 120V Replace the three resistors with one equivalent resistor 16W 32W 8W32W

120V Find the resistance in Series: R total = R 1 + R 2 + etc. R 123-4 =8 + 16 R 1234 =24 16W 8W

Make a table with the following: Make chart: R I V 16W R 1 16 120V R 2 16 16W 32W 32W R 3 32 R 4 32 R 234 8 R 1234 24 120

Make chart: These are in parallel so their voltage is the same along with the total voltage. In Parallel circuits: V 1 = V 2 = V 3 = etc. 120V 16W 16W 32W 32W All these numbers will be the same. R I V R 1 16 R 2 16 R 3 32 R 4 32 R 234 8 R 1234 24 120

120V Make chart: 16W 8W All these numbers will be the same. These are in series so their current is the same along with the total current: I 1 = I 2 = I 3 = etc. R I V R 1 16 R 2 16 R 3 32 R 4 32 R 234 8 R 1234 24 120

Fill out the chart with V=IR V = IR 120 = I (24) I = 5 A V = IR V = (5) (16) V = 80 V R I V R 1 16 5 80 R 2 16 R 3 32 R 4 32 R 234 8 5 R 1234 24 5 120

Fill out the chart with V=IR V = IR 120 = I (24) I = 5 A V = IR V = (5) (8) V = 40 V V = IR V = (5) (16) V = 80 V V = IR 40 = I (16) I = 2.5 A V = IR 40 = I (32) I = 1.25 A R I V R 1 16 5 80 R 2 16 2.5 40 R 3 32 40 R 4 32 40 R 234 8 5 40 R 1234 24 5 120

Fill out the chart with V=IR V = IR 120 = I (24) I = 5 A V = IR V = (5) (8) V = 40 V V = IR V = (5) (16) V = 80 V V = IR 40 = I (16) I = 2.5 A V = IR 40 = I (32) I = 1.25 A R I V R 1 16 5 80 R 2 16 2.5 40 R 3 32 1.25 40 R 4 32 1.25 40 R 234 8 5 40 R 1234 24 5 120

Another way to do the problem (without the chart) I=V/R 120V I=120v/24W I=5 amps 24W

V=IR V=(5)(16) V=80volts 16W 80volts 120V V=IR V=(5)(8) V=40volts 5amps 8W 40volts 120volts

I=V/R =40volts/16 W =2.5 amps 5 amps 16W 80volts 120V I=V/R =40volts/32 W =1.25 amps 16W 32W 32W 40 volts 5 amps

When the series circuit shown is connected, Bulb A is brighter than Bulb B. If the positions of the bulbs were reversed 1. Bulb A would again be brighter 2. Bulb B would be brighter 3. They would be the same The bulbs are connected in series, so the same current passes through both of them. Different brightnesses indicate different filament resistances. Bulb A is NOT brighter because it is first in line for the current of the battery! After all, electrons deliver the energy, and they flow from negative to positive --- in the opposite direction!

P. O. D. 5: Find the voltage and current for each resistor. 3 W 3 W 6 W 6 W 4 W 12 W 2 W 18 volts

3W 3W 4W 12W 6W 6W 2W 18 volts

3W 3W 3W 4W 12W 2W 18 volts

6W 3W 4W 12W 2W 18 volts

6W 3W 1 1 = + R total R 1 1 R 2 4W 12W 2W 1 R total = 1 4 + 1 12 18 volts R total =3W

6W 3W 1 1 = + R total R 1 1 R 2 3W 2W 1 R total = 1 4 + 1 12 18 volts R total =3W

6W 3W 3W 2W 18 volts

6W 3W 5W 18 volts

6W 1 R total R total 3W 1 = + 6 1 5 = 2. 73W 5W 18 volts

3W 2.73W 18 volts

5.73W 18 volts

Now, find the total current flowing I V I = R 18volts = 5.73W I = 3. 14 amps 5.73W 18 volts

9.42volts 3W 3W V=IR V=(3.14)(3W) 4W V=9.42 12W 6W 6W 2W 18 volts

18-9.42 8.57volts 9.42volts 3W 3.14 amps 3W 4W 12W 6W 6W 2W 18 volts

18-9.42 8.57volts 9.42volts 6W 3W 3.14 amps 4W 12W 2W 18 volts

18-9.42 8.57volts 9.42volts 6W 3W 3.14 amps 5W 18 volts

18-9.42 8.57volts 9.42volts I = 3W I = V R 8.57volts 6W I =1. 43amps 6W 5W 18 volts

18-9.42 8.57volts 9.42volts 3W 3.14 amps 6W 1.43 amps 5W 1.71 amps 18 volts

18-9.42 8.57volts 9.42volts 3W 3.14 amps 1.71 amps V=IR V=(1.71)(2) V=3.42volts 6W 1.43 amps 4W 12W 18 volts 3.42Volts 2W 1.71 amps

18-9.42 8.57volts 9.42volts 6W 1.43 amps 3W 3.14 amps 1.71 amps 5.15 volts 4W 12W 3.42Volts 2W 1.71 amps 18 volts

I=V/R I=5.15volts/12W 9.42volts I= 0.43 amps 3W 3.14 amps 1.71 amps 6W 4W 18-9.42 5.15 volts 8.57volts 12W 0.43 amps 1.43 amps 3.42Volts 2W 1.71 amps 18 volts

I=V/R I=5.15volts/4W 9.42volts I= 1.28 amps 3W 3.14 amps 1.71 amps 6W 4W 18-9.42 Or 8.57volts 1.71 amps 0.43 = 1.28 amps 5.15 volts 12W 0.43 amps 3.42Volts 2W 1.71 amps 18 volts

3W 3W 4W 12W 6W 6W 2W 18 volts

3W 3W 4W 12W 6W 6W 2W 18 volts Q

Given: R1=1W; R2=2 W; R3=3 W. Rank the bulbs according to their relative brightness 1. R 1 > R 2 > R 3 2. R 1 > R 2 = R 3 3. R 1 = R 2 > R 3 4. R 1 < R 2 < R 3 R 1 R 2 R 3 5. R 1 = R 2 = R 3

Given: R1=1W; R2=2 W; R3=3 W. Rank the bulbs according to their relative brightness 15 1. R 1 > R 2 > R 3 2. R 1 > R 2 = R 3 3. R 1 = R 2 > R 3 4. R 1 < R 2 < R 3 R 1 R 2 R 3 5. R 1 = R 2 = R 3 P = IV = I 2 R = V 2 R Q

If the four light bulbs in the figure below are identical, which circuit puts out more total light? 1. I 2. II 3. Same Circuit II

If the four light bulbs in the figure below are identical, which circuit puts out more total light? 1. I 2. II 3. Same Circuit II The resistance of two light bulbs in parallel in smaller than that of two bulbs in series. Thus the current through the battery is greater for circuit I than for circuit II. Since the power dissipated is the product of current and voltage, it follows that more is dissipated in circuit I.