3/6 do now• A piece of copper wire with a cross-sectional area of

3.0 x 10-5 meter2 is 25 meters long. How would changing the length of this copper wire change its resistivity?

Due:20.2 notes

Ω work:Castle learning

Unit test – 3/14Questions from packets

Project – 3/14

objectivesBe able to

1.Sketch diagrams of series circuits including proper placement of meters.

2.VIR charts and Ohm’s Law to solve series circuits problems.

3.Determine the power or electrical energy used by a circuit component or an entire circuit.

4.Determine the effect of adding or removing resistors to the rest of a circuit.

4.2.4 Series Circuits

One Thing at a Time

Definitions• series circuit – a circuit in which two or more

elements are connected end-to-end so that a single loop of current is formed.

Series Circuit Rules• equivalent Resistance – more resistors = more resistance

• Req = R1 + R2 + …

• current – same throughout circuit• I = I1 = I2 = …

• voltage – voltages add up• V = V1 + V2 + …

• All circuit components and the circuit as a whole must obey Ohm’s Law

• Since there is only one current path in a series circuit, the current is the same through each resistor.

• ______________________

Current

Charge flows together through the external circuit at a rate which is everywhere the same. The current is no greater at one location as it is at another location.

Ibattery = I1 = I2 = I3 = ..

Equivalent Resistance• The equivalent resistance of a circuit is the amount of

resistance which a single resistor would need in order to equal the overall affect of the collection of resistors which are present in the circuit.

•The equivalent resistance in a series circuit is the sum of the circuit’s resistances:

____________________________________Req = R1 + R2 + R3 + ...

Potential Difference and Voltage Drops

• The sum of the potential differences across the individual resistors equals the applied potential difference at the terminals.

• _______________________________∆Vbattery = ∆V1 + ∆V2 + ∆V3 + ...

Mathematical Analysis of Series Circuits

Ibattery= I1 = I2 = I3 = ...

Req = R1 + R2 + R3 + ...

Vbattery =  V1 +  V2 +  V3 + ...

V1 = I • R1     V2 = I • R2     V3 = I • R3V1

V2

V3

• All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

7.5 V

5.0 Ω 8.0 Ω 2.0 Ω

R1 R2 R3

V (V) I (A) R (Ω)R1

R2

R3

Req15

5.08.02.0

0.5

0.50.50.5

7.5

2.54.01.0

50 Ω 120 Ω 150 Ω

R1 R2 R3

V (V) I (A) R (Ω)R1

R2

R3

Req320

50120150

1.5

1.51.51.5

480

75180225

1.5A

Example

• A series circuit has a total resistance of 1.00 x 102 ohms and an applied potential difference of 2.00 x 102 volts. What is the amount of charge passing any point in the circuit in 2.00 seconds?

I = V / R = 2.00 x 102 V / 1.00 x 102 Ω

I = 2.00 A

I = Q / t

2.00 A = Q / 2.00 s Q = 4.00 C

End of 4.2.4 – PRACTICE

3/7 do now• Consider the physical quantity 200 m North.

1. What is the magnitude of this number?

2. What is the order of the magnitude of this quantity?

Ω work:Castle learningPractice packet 4.2.4 – due Mon.Reading 21.1-22.1 due Tue.

Unit test – 3/14Questions from packets

Project – 3/14

objectivesBe able to

1.Sketch diagrams of parallel circuits including proper placement of meters.

2.VIR charts and Ohm’s Law to solve parallel circuits problems.

3.Determine the power or electrical energy used by a circuit component or an entire circuit.

4.Determine the effect of adding or removing resistors to the rest of a circuit.

4.2.5 Parallel Circuits

Wiring for Voltage

Definitions• parallel circuit – a circuit in which two or more

elements are connected so that each has its own current loop.

1. More current flows through the smaller resistor. (More charges take the easiest path.)

2. The potential difference of different resistors are the same, they all have the same drop.

3. By the time each charge makes it back to the battery, it has lost all the electrical energy given to it by the battery.

Parallel Circuit Rules• equivalent Resistance – more resistors = less resistance

• 1/Req = 1/R1 + 1/R2 + …

• current – currents add up• I = I1 + I2 + …

• voltage – voltages same for each resistor• V = V1 = V2 = …

• All circuit components and the circuit as a whole must obey Ohm’s Law

Current• In a parallel circuit, charge divides up into separate branches

such that there can be more current in one branch than there is in another. Nonetheless, when taken as a whole, the total amount of current in all the branches when added together is the same as the amount of current at locations outside the branches.

Itotal = I1 + I2 + I3 + ...

Junction Rule• The total current flowing into and out of a junction must

be the same

10 A

4.0 A

?6.0 A

Junction Rule

?

2.0 A

10 A?

6.0 A

4.0 A6.0 A

Example 1• The diagram shows the current in three of the branches of

a direct current electric circuit. The current in the fourth branch, between junction P and point W, must be

1. 1 A toward point W

2. 1 A toward point P

3. 7 A toward point W

4. 7 A toward point P  

Example 2

• The diagram shows a current in a segment of a direct current circuit.  What is the reading of ammeter A?

• The equivalent resistance (total resistance) of a circuit is the amount of resistance which a single resistor would need in order to equal the overall effect of the collection of resistors which are present in the circuit. For parallel circuits, the mathematical formula for computing the equivalent resistance (Req) is

where R1, R2, and R3 are the resistance values of the individual resistors which are connected in parallel.

321

1111

RRRReq

Equivalent Resistance

• For parallel circuit, adding more resistors you add the less resistance you have.

Example 3 – determine equivalent R

Note: the equivalent resistance is less than any single resistance in the circuit.

3.2

12

1

7

1

5

11

eq

eq

R

R

Example 4• Resistors R1 and R2 have an equivalent

resistance of 6 ohms when connected as shown.  What is the resistance of R1?

1. 3 ohms

2. 4 ohms

3. 5 ohms

4. 8 ohms

Since the equivalent resistance is smaller than any single resistance in the parallel circuit, the answer is 8 ohms

Example 5• Resistors R1 and R2 have the same resistance.

When they are connected together as shown, they have an equivalent resistance of 4 ohms.  What is the resistance of R1?

Since R1 = R2

1/4 Ω = 1/R1 + 1/R1 = 2/R1

R1 = 8 Ω

Note: the individual resistance is bigger than the total resistance in the parallel circuit.

Voltage Drops for Parallel Branches• The total voltage drop in the external circuit is equal to

the gain in voltage as a charge passes through the internal circuit. In a parallel circuit, a charge does not pass through every resistor; rather, it passes through a single resistor. Thus, the entire voltage drop across that resistor must match the battery voltage. It matters not whether the charge passes through resistor 1, resistor 2, or resistor 3, the voltage drop across the resistor which it chooses to pass through must equal the voltage of the battery. Put in equation form, this principle would be expressed as

Vbattery = V1 = V2 = V3 = ..

I1 = V / R1

I2 = V / R2

I3 = V / R3

All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

eqeq R

VI

V (V) I (A) R (Ω)R1

R2

R3

Req10

303030

6.0

2.02.02.0

60

606060

R1 = 30 Ω

R2 = 30 Ω

R3 = 30 Ω

60 V

V (V) I (A) R (Ω)R1

R2

R3

Req5.9

205010

0.85

0.250.10.5

5.0

5.05.05.0 R1 = 20 Ω

R2 = 50 Ω

R3 = 10 Ω0.5 A

Example 6

• In the diagram, what is the potential difference across the 3.0-ohm resistor?

End of 4.2.5 – PRACTICE

Objectives – Lab 16• Objective

• Material

• Data table

• Answer questions

3/10 do now1. The diagram represents a series circuit containing three

resistors. What is the current through resistor R2? [show work]

Due:Packet 4.2.4

Ω work:Castle learningReading 21.1-22.1

Unit test – 3/14Questions from packets

Project – 3/14

Objectives Know:

−The definition for each type of circuit.

−The rules for current; voltage; and equivalent resistance in each type of circuit.

Understand

-Effect of adding resistances to a series circuit

-Effect of adding resistances to a parallel circuit

Be able to

−Select/sketch diagrams of series and parallel circuits including proper placement of meters.

−Use VIR charts and Ohm’s Law to solve series and parallel circuits.

−Determine the power or electrical energy used by a circuit component or an entire circuit.

−Use the Junction Rule to determine an unknown current.

−Determine which of a system of resistances will minimize/maximize equivalent resistance.

−Determine the effects of switches on current; voltage; and equivalent resistance in circuits.

Example 1• Circuit A and circuit B are shown in the

diagram. Compared to the total resistance of circuit A, the total resistance of circuit B is

1. less

2. greater

3. the same

Example 2• In the diagram of a parallel circuit,

ammeter A measures the current supplied by the 110-volt source.  What is the current measured by ammeter A?

11 A

Example 3• Two resistors are connected to a source of

voltage as shown in the diagram. At which position should an ammeter be placed to measure the current passing only through resistor R1?

1.   position 1

2.   position 2

3.   position 3

4.   position 4

Example 4• Three ammeters are placed in a circuit as

shown in the diagram.  If A1 reads 5.0

amperes and A2 reads 2.0 amperes, what

does A3 read?

3 A

Example 5

• In the circuit shown in the diagram, which is the correct reading for meter V2?

Example 6• Which circuit could be used to determine the

total current and potential difference of a parallel circuit?

A B

C D

Example 7

• In the circuit shown in the diagram, what is the potential difference of the source?

Example 8• Which circuit below would have the lowest

voltmeter reading?

A B

C D

Example 9• In which pair of circuits shown in the diagram could the

readings of voltmeters V1 and V2 and ammeter A be correct?

1. A and B

2. B and C

3. C and D

4. A and D

Example 10• Which statement about ammeters and voltmeters is

correct?1. The internal resistance of both meters should be low. 2. Both meters should have a negligible effect on the

circuit being measured. 3. The potential drop across both meters should be

made as large as possible. 4. The scale range on both meters must be the same.

Example 11• In the diagram below, lamps L1 and L2 are

connected to a constant voltage power supply. If lamp L1 burns out,

1. What will happen to the equivalent resistance of the circuit?

2. What will happen to the total current of the circuit?

3. What will happen to the brightness of L2 ?

Example 12• Identical resistors (R) are connected across the same

12-volt battery. Which circuit uses the greatest power?

BA

C D

Class work• Regents review page 117 #49-99