Download (A) R

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 – 3/14
Questions from packets
Project – 3/14
objectives
Be 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.
One Thing at a Time
4.2.4 Series Circuits
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
Current
• Since there is only one current path in a series
circuit, the current is the same through each
resistor.
Ibattery = I1 = I2 = I3 = ..
•
______________________
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.
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.
∆V
=
∆V
+
∆V
+
∆V
+
...
battery
1
2
3
• _______________________________
Mathematical Analysis of Series
Circuits
Ibattery= I1 = I2 = I3 = ...
Req = R1 + R2 + R3 + ...
Vbattery = V1 + V2 + V3 + ...
• All COMPONENTS and the WHOLE CIRCUIT obey
Ohm’s Law
V1
V =I•R
V =I•R
V =I•R
1
1
2
2
3
3
V2
V3
5.0 Ω
8.0 Ω
2.0 Ω
R1
R2
R3
7.5 V
R1
R2
R3
Req
V (V)
2.5
4.0
1.0
7.5
I (A)
0.5
0.5
0.5
0.5
R (Ω)
5.0
8.0
2.0
15
50 Ω
120 Ω
150 Ω
R1
R2
R3
1.5A
R1
R2
R3
Req
V (V)
75
180
225
480
I (A)
1.5
1.5
1.5
1.5
R (Ω)
50
120
150
320
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 learning
Practice packet 4.2.4 –
due Mon.
Reading 21.1-22.1 due
Tue.
Unit test – 3/14
Questions from packets
Project – 3/14
objectives
Be 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.
Wiring for Voltage
4.2.5 Parallel Circuits
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
6.0? A
10 A
4.0 A
Junction Rule
6.0 A
6.0? A
4.0? A
2.0 A
10 A
Example 1
•
1.
2.
3.
4.
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 A toward point W
1 A toward point P
7 A toward point W
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?
Equivalent Resistance
• 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
1
1
1
1
 

Req R1 R2 R3
where R1, R2, and R3 are the resistance values of the
individual resistors which are connected in parallel.
• For parallel circuit, adding more resistors you
add the less resistance you have.
Example 3 – determine equivalent R
1
1
1
1



Req 5 7 12
Req  2.3
Note: the equivalent resistance is less
than any single resistance in the
circuit.
Example 4
•
1.
2.
3.
4.
Resistors R1 and R2 have an equivalent
resistance of 6 ohms when connected as
shown. What is the resistance of R1?
3 ohms
4 ohms
5 ohms
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 V
battery = V1 = V2 = V3 = ..
All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law
I1 = V / R1
I2 = V / R2
I3 = V / R3
V
I eq 
Req
R1
R2
R3
Req
V (V)
60
60
60
60
I (A)
2.0
2.0
2.0
6.0
R (Ω)
30
30
30
10
R3 = 30 Ω
R2 = 30 Ω
R1 = 30 Ω
60 V
0.5 A
R1
R2
R3
Req
V (V)
5.0
5.0
5.0
5.0
I (A) R (Ω)
0.25
20
0.1
50
0.5
10
0.85 5.9
R3 = 10 Ω
R2 = 50 Ω
R1 = 20 Ω
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 now
1. 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 learning
Reading 21.1-22.1
Unit test – 3/14
Questions 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?
3A
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
C
B
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
•
1.
2.
3.
4.
In which pair of circuits shown in the diagram could the
readings of voltmeters V1 and V2 and ammeter A be correct?
A and B
B and C
C and D
A and D
Example 10
•
1.
2.
3.
4.
Which statement about ammeters and voltmeters is
correct?
The internal resistance of both meters should be
low.
Both meters should have a negligible effect on the
circuit being measured.
The potential drop across both meters should be
made as large as possible.
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?
A
C
B
D
Class work
• Regents review page 117 #49-99