CIRCUITS

1
CIRCUITS
2
The Electric Battery
A battery transforms chemical energy into
electrical energy. Chemical reactions within the
cell create a potential difference between the
terminals This potential difference can be
maintained even if a current is kept flowing.
3
The Electric Battery
Several cells connected together make a battery,
although now we refer to a single cell as a
battery as well.
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
Ohms Law Resistance and Resistors
Experimentally, it is found that the current in a
wire is proportional to the potential difference
between its ends
8
Ohms Law Resistance and Resistors
The ratio of voltage to current is called the
resistance
I V/R
9
Ohms Law Resistance and Resistors

• Some clarifications
• Batteries maintain a (nearly) constant potential
  difference the current varies.
• Resistance is a property of a material or
  device.
• Current is not a vector but it does have a
  direction.
• Current and charge do not get used up. Whatever
  charge goes in one end of a circuit comes out the
  other end.

10

• A battery is connected to a resistor. As charge
  flows, the chemical energy of the battery is
  dissipated as
• current.
• voltage.
• charge.
• thermal energy.

Slide 22-10
11
Answer

• A battery is connected to a resistor. As charge
  flows, the chemical energy of the battery is
  dissipated as
• current.
• voltage.
• charge.
• thermal energy.

Slide 22-11
12

• A battery is connected to a resistor. Increasing
  the resistance of the resistor will
• increase the current in the circuit.
• decrease the current in the circuit.
• not affect the current in the circuit.

Slide 22-8
13
Answer

• A battery is connected to a resistor. Increasing
  the resistance of the resistor will
• increase the current in the circuit.
• decrease the current in the circuit.
• not affect the current in the circuit.

Slide 22-9
14
Electric Power
Power, as in kinematics, is the energy
transformed by a device per unit time
15
Energy and Power in Resistors
Slide 22-31
16
Electric Power
The unit of power is the watt, W. For ohmic
devices, we can make the substitutions

17
Electric Power
The unit of power is the watt, W. For ohmic
devices, we can make the substitutions
18
Electric Power
What you pay for on your electric bill is not
power, but energy the power consumption
multiplied by the time. We have been measuring
energy in joules, but the electric company
measures it in kilowatt-hours, kWh.
19
Power in Household Circuits
The wires used in homes to carry electricity have
very low resistance. However, if the current is
high enough, the power will increase and the
wires can become hot enough to start a fire. To
avoid this, we use fuses or circuit breakers,
which disconnect when the current goes above a
predetermined value.
20
Power in Circuits
Slide 22-30
21
Checking Understanding

• A resistor is connected to a 3.0 V battery the
  power dissipated in the resistor is 1.0 W. The
  battery is traded for a 6.0 V battery. The power
  dissipated by the resistor is now
• 1.0 W
• 2.0 W
• 3.0 W
• 4.0 W

Slide 22-32
22
Answer

• A resistor is connected to a 3.0 V battery the
  power dissipated in the resistor is 1.0 W. The
  battery is traded for a 6.0 V battery. The power
  dissipated by the resistor is now
• 1.0 W
• 2.0 W
• 3.0 W
• 4.0 W

Slide 22-33
23
Problem
An electric blanket has a wire that runs through
the interior. A current causes energy to be
dissipated in the wire, warming the blanket. A
new, low-voltage electric blanket is rated to be
used at 18 V. It dissipates a power of 82 W. What
is the resistance of the wire that runs through
the blanket?
Slide 22-34
24
Problem

• Standard electric outlets in the United States
  run at 120 V in England, outlets are 230 V. An
  electric kettle has a coiled wire inside that
  dissipates power when it carries a current,
  warming the water in the kettle. A kettle
  designed for use in England carries 13 A when
  connected to a 230 V outlet.
• 
  
• What is the resistance of the wire?
• What power is dissipated when the kettle is
  running?
• The kettle can hold 1.7 L of water. Assume that
  all power goes to heating the water. How long
  will it take for the kettle to heat the water
  from 20ºC to 100ºC?

Slide 22-37
25
Question

• A set of lightbulbs have different rated voltage
  and power, as in the table below. Which one has
  lowest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

Slide 22-41
26
Answer

• 2. A set of lightbulbs have different rated
  voltage and power, as in the table below. Which
  one has lowest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

Slide 22-42
27

• 4. In Trial 1, a battery is connected to a single
  lightbulb and the brightness noted. Now, in Trial
  2, a second, identical, lightbulb is added. How
  does the brightness of these two bulbs compare to
  the brightness of the single bulb in Trial 1?
• The brightness is greater.
• The brightness is the same.
• The brightness is less.

Slide 22-45
28
Answer

• 4. In Trial 1, a battery is connected to a single
  lightbulb and the brightness noted. Now, in Trial
  2, a second, identical, lightbulb is added. How
  does the brightness of these two bulbs compare to
  the brightness of the single bulb in Trial 1?
• The brightness is greater.
• The brightness is the same.
• The brightness is less.

Slide 22-46
29
Problem

• How much time does it take for 1.0 C to flow
  through each of the following circuit elements?
• A 60 W reading light connected to 120 V.
• A 60 W automobile headlamp connected to 12 V.

Slide 22-47
30
Resistors in Series
A series connection has a single path from the
battery, through each circuit element in turn,
then back to the battery.
31
Resistors in Series
The current through each resistor is the same
the voltage depends on the resistance. The sum of
the voltage drops across the resistors equals the
battery voltage.
V I ( R1 R2 R3)
32
Resistors in Series
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit).
33
Resistors in Parallel
A parallel connection splits the current the
voltage across each resistor is the same
34
Resistors in Parallel
At A I I1 I2 I3
35
Resistors in Parallel
The total current is the sum of the currents
across each resistor
36
Resistors in Parallel
This gives the reciprocal of the equivalent
resistance
For two resistors in parallel 1/Req 1/R 1/R
2/R Req R/2 Twice as much current can flow
37
Resistors in Parallel
An analogy using water may be helpful in
visualizing parallel circuits The height h is
same for both (e.g. equal V). Twice as much water
will flow with both open. Twice as much current
will flow with 2 Rs parallel.
38
Review

• Exam on Monday
• Covers all lectures, HW and readings from Wed.
  Oct 13 until Wed. Nov.3
• Only MC questions from Chemistry material (Brown
  readings)

39
Review

• An electron volt (eV) is a unit of
• A) Charge
• B) current
• C) potential
• D) energy
• E) capacitance

40
Review

• An electron volt (eV) is a unit of
• A) Charge
• B) current
• C) potential
• D) energy
• E) capacitance
• An electron volt is the energy change when a
  particle of charge e moves through a potential
  difference of 1 V
• 1 eV 1.6 x 10-19J

41
Review

• What is electric potential?
• Analogy- Escalator
• How much work do we do
• when we send boxes of
• mass m1, m2, m3, up
• m1gh m2gh m3gh
• Easier to sum the masses
• m1 m2 m3 .. And then
• multiply by gh

42
Review
Similar for charges. Just as a mass gains or
loses gravitational PE as It is raised or lowered
an electric charge gains or loses electrical PE
as it moves from a region of one potential V1 to
another of V2 A charge q changes its energy by
q( V2-V1) A charge e passing through a 6V
Battery changes its energy by 6eV
43
Review

• Placing charges in a region changes the space in
  that region.
• If the Moon were only 240 miles from E instead of
  240,000 we things would be different.
• Placing charge here changes space
• here.
• This change is recorded as E

44
Example Problems
There is a current of 1.0 A in the circuit below.
What is the resistance of the unknown circuit
element?
Slide 23-24
45
Example Problems
What is the current out of the battery?
Slide 23-24
46
Questions

• In the circuit below, the switch is initially
  open and bulbs A and B are of equal brightness.
  When the switch is closed, what happens to the
  brightness of the two bulbs?
• The brightness of the bulbs is not affected.
• Bulb A becomes brighter, bulb B dimmer.
• Bulb B becomes brighter, bulb A dimmer.
• Both bulbs become brighter.

Slide 23-45
47
Answer

• In the circuit below, the switch is initially
  open and bulbs A and B are of equal brightness.
  When the switch is closed, what happens to the
  brightness of the two bulbs?
• The brightness of the bulbs is not affected.
• Bulb A becomes brighter, bulb B dimmer.
• Bulb B becomes brighter, bulb A dimmer.
• Both bulbs become brighter.

Slide 23-46
48
Kirchhoffs Rules
Some circuits cannot be broken down into series
and parallel connections.
49
Kirchhoffs Junction Law
Slide 23-15
50
Kirchhoffs Rules
For these circuits we use Kirchhoffs
rules. Junction rule The sum of currents
entering a junction equals the sum of the
currents leaving it.
At a I3 I1 I2 At d I1 I2 I3
51
Checking Understanding

• The diagram below shows a segment of a circuit.
  What is the current in the 200? resistor?
• 0.5 A
• 1.0 A
• 1.5 A
• 2.0 A
• There is not enough information to decide.

Slide 23-18
52
Answer

• The diagram below shows a segment of a circuit.
  What is the current in the 200? resistor?
• 0.5 A
• 1.0 A
• 1.5 A
• 2.0 A
• There is not enough information to decide.

Slide 23-19
53
(No Transcript)
54
Kirchhoffs Loop Law
Slide 23-16
55
Kirchhoffs Rules
Loop rule The sum of the changes in potential
around a closed loop is zero.
56
Kirchhoffs Rules

• Problem Solving Kirchhoffs Rules
• Label each current.
• Identify unknowns.
• Assign direction to current
• Go around the loop
• Current to ?V E
• Current to - ?V -E
• Apply junction and loop rules you will need as
  many independent equations as there are unknowns.
• Solve the equations, being careful with signs.

57
EMFs in Series and in Parallel Charging a
Battery
EMFs in series in the same direction total
voltage is the sum of the separate voltages
58
EMFs in Series and in Parallel Charging a
Battery
EMFs in series, opposite direction total voltage
is the difference, but the lower-voltage battery
is charged.
59
Checking Understanding

• The diagram below shows a circuit with two
  batteries and three resistors. What is the
  potential difference across the 200?
  resistor?
• 2.0 V
• 3.0 V
• 4.5 V
• 7.5 V
• There is not enough information to decide.

Slide 23-20
60
Answer

• The diagram below shows a circuit with two
  batteries and three resistors. What is the
  potential difference across the 200?
  resistor?
• 2.0 V
• 3.0 V
• 4.5 V
• 7.5 V
• There is not enough information to decide.

Slide 23-21
61
Electric Hazards
Even very small currents 10 to 100 mA can be
dangerous, disrupting the nervous system. Larger
currents may also cause burns. Household voltage
can be lethal if you are wet and in good contact
with the ground. Be careful!
62
Electric Hazards
A person receiving a shock has become part of a
complete circuit.
63
Electric Hazards
Faulty wiring and improper grounding can be
hazardous. Make sure electrical work is done by a
professional.
64
Electric Hazards
The safest plugs are those with three prongs
they have a separate ground line. Here is an
example of household wiring colors can vary,
though! Be sure you know which is the hot wire
before you do anything.
65
Summary
Slide 23-43
66
Additional Example Problems

• In the circuit shown below
• How much power is dissipated by the 12 O
  resistor?
• What is the value of the potential at points a,
  b, c, and d?

Slide 23-51