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ELECTRIC CURRENT
Chapter 23:
Flow of Charge
• When there is a potential difference—
charge flows from one end to the other.
The flow of charge persists for as long as
there is a potential difference.
Water flow.
Electric Current
• Electric Current: steady
flow of electric charge.
• In circuits of metal wires,
electrons make up the flow of
charge
• Convention: current has
the direction of the flow of
positive charges.
Definition of CurrentI
• Current (I) =amount of charge that
passes through a cross sectional area
of a conductor in one unit of time.
Charge
Charge
I=
Cross-sectional
area
Time
Unit of measurement:
Ampere (A)
Unit of Current
• The rate of electrical flow is measured in
amperes. One ampere is a rate of flow equal to
1 coulomb of charge per second. (Recall that 1
coulomb, the standard unit of charge, is the
electric charge of 6.25 billion billion electrons.)
• In a wire that carries 5 amperes, for example, 5
coulombs of charge pass any cross section in
the wire each second.
• In a wire that carries 10 amperes, twice as many
electrons pass any cross section each second.
Electric Current Example
How many electrons flow through a cross
sectional area of a conductor in 5s, if it is
traveled by a current of 3.2 A
1. Find the total charge:
I
Ch arg e
 Ch arg e  I  Time  3.2 A  5s  16C
Time
2. Find the number of electrons N using the
charge of an electron e=1.6 x 10-19C
Ch arg e
16C
20
Number 


10
e
1.6 10 19 C
Current (continuation)
• Source: converts other forms of energy
into electric energy.
High
Poten
tial
Flow of “+” charge
A
Source
Low
B Poten
tial
Analogy
• A ball rolling down a hill
High
Low
Difference of height causes the ball to
roll down the hill.
Sources
High
Potential

Low
Potential
Batteries (Voltage sources):
Purpose is to provide a constant potential
+ OR
difference (voltage) between two points.
+
V
-
Sources
• Electromagnetic induction: conversion of
electromagnetic energy into electricity.
• Piezoelectric: mechanical stress on certain
crystals creates a difference of potential.
• Photoelectric effect: light energy is
converted into electric energy.
• Batteries: convert chemical energy into
electric energy.
Voltage
• A useful meter is a
multimeter, which
can measure voltage or
current, and sometimes
resistance.
• To measure voltage, the
meter’s probes are
touched to two places in a
circuit or across a battery.
Measuring current
• If you want to measure
current you must force the
current to pass through
the meter.
• Multimeters can measure
two types of current:
alternating current (AC)
and direct current (DC).
Resistance
• Resistance (R): opposition to the flow of
the electric current. Caused by
collisions b/w electrons and the atoms
of the metal.
• Measured in ohms Ω.
• Depends upon type of material
(resistivity), proportional to length,
inversely proportional to thickness
(cross sectional area A).
Resistance
• Increase the length, flow of electrons impeded (more
collisions)
• Increase the cross sectional area, flow facilitated (more
space)
• The structure of this relation is identical to heat flow
through materials … think of a window for an intuitive
example
How thick?
or
How big?
What’s it made of?
Resistance Continuation
• R is proportional to the temperature. At
low temperatures conductors exhibit
low resistance (superconductors).
• Causes electric energy to turn into
heat.
Electric Circuit
• Electric Circuit: complete path through
which a current can flow. Made of a
source of current (battery), connecting
wires, and an electricity user.
User
Wires
- S +
I
Simple Electric Circuit Analogy
Electric Circuits
• When drawing a circuit diagram, symbols are
used to represent each part of the circuit.
Electrical Symbols
• Electrical symbols are
quicker and easier to
draw than realistic
pictures of the
components.
Ohm’s Law
• Determined experimentally the relationship
between current and voltage in a circuit.
Ohm’s Law
• I=V/R
V
R
A
S
Source: provides electric energy.
V - voltmeter: measures voltage (parallel)
A - ammeter: measures electric current (series)
Ohm’s Law Examples
•
•
•
•
For a given circuit of constant resistance, current and voltage are
proportional to each other. This means we'll get twice the current for
twice the voltage. The greater the voltage, the greater the current.
But if the resistance is doubled for a circuit, the current will be half
what it would be otherwise. The greater the resistance, the smaller the
current.
Ohm's law tells us that a potential difference of 1 volt established
across a circuit that has a resistance of 1 ohm will produce a current
of 1 ampere.
If 12 volts are impressed across the same circuit, the current will be 12
amperes.
The resistance of a typical lamp cord is much less than 1 ohm, while a
typical light bulb has a resistance of more than 100 ohms. An iron or
electric toaster has a resistance of 15–20 ohms. Inside electrical
devices such as radio and television receivers, current is regulated by
circuit elements called resistors, whose resistance may be a few ohms
or millions of ohms.
Examples Numerical
1. How much current will flow through a lamp that
has a resistance of 60 Ω when 12 V are impressed
across it?
12V 1
Current 
 A  0.2 A
60 5
2. What is the resistance of an electric frying pan that
draws 12 A when connected to a 120-V circuit?
120V
120V
12 A 
 Re sis tan ce 
 10
Re sis tan ce
12 A
Ohm's Law and Electric Shock
•
•
•
The damaging effects of shock
are the result of current (not
voltage!) passing through the
body.
The resistance of one's body
depends on its condition and
ranges from about 100 ohms if
soaked with salt water to about
500,000 ohms if the skin is very
dry.
If we touch the two electrodes of
a battery with dry fingers,
completing the circuit from one
hand to the other, we can
expect to offer a resistance of
about 100,000 ohms. We
usually cannot feel the current
produced by 12 volts, and 24
volts just barely tingles. If our
skin is moist, 24 volts can be
quite uncomfortable.
Effect of Electric Currents on the Body
Current (A)
Effect
0.001
Can be felt
0.005
Is painful
0.010
Causes involuntary
muscle contractions
(spasms)
0.015
Causes loss of
muscle control
0.070
If through the heart,
serious disruption;
probably fatal if
current lasts for more
than 1 s
1. At a resistance of 100,000 Ω, what will be the current in your body if you touch the
terminals of a 12-volt battery?
2. If your skin is very moist—so that your resistance is only 1000 Ω—and you touch
the terminals of a 12-volt battery, how much current do you receive?
1. 0.00012 A
2. 0.012 A
Direct Current and Alternating
Current
• direct current (dc): the
charges are flowing in
one direction.
• Alternating current (ac)
charges are flowing first
in one direction and then
in the opposite direction.
The current changes
direction constantly at a
given frequency.
Drift Velocity
• The motion of the electrons cased by the electric
field is affected by collisions with the atoms the
metal is made of.
• Therefore, the velocity in the direction of the field
along the wire called drift velocity is extremely
low (hundredth of a centimeter per second).
Electric Field
Electric Power
• The rate at which electric energy is delivered or
used in an electric circuit is called electric
power. It is converted into another form such as
mechanical energy, heat, or light.
Electric Power (2)
• If a lamp rated at 120 watts operates on a 120-volt line,
it will draw a current of 1 ampere (120 watts = 1 ampere
× 120 volts).
• A 60-watt lamp draws 1/2 ampere on a 120-volt line.
• Calculating the cost of electrical energy:
A kilowatt is 1000 watts, and a kilowatt-hour represents
the amount of energy consumed in 1 hour at the rate of 1
kilowatt. Therefore, in a locality where electric energy
costs 5 cents per kilowatt-hour, a 100-watt electric light
bulb can be run for 10 hours at a cost of 5 cents, or a
half cent for each hour. A toaster or iron, which draws
much more current and therefore much more energy,
costs about ten times as much to operate.
Power Calculations
• The power and voltage on the light bulb
read “100 W , 120 V.” How many amperes
will flow through the bulb?
100 W = current x 120 V
current =100/120 = 5/6 A = .83 A
More Calculations
• 1. If a 120-V line to a socket is limited to 15 A by a safety
fuse, will it operate a 1200-W hair dryer?
2. At 10¢/kWh, what does it cost to operate the 1200-W
hair dryer for 1 h?
Power = 15 A x 120 V = 1800 Watt (yes!)
1200 Watt = 1.2 KWatt
Cost = 1.2 KW x 1h x 0.1$ = 0.12$
ConcepTest 17.1
Which is the correct way to
light the lightbulb with the
Connect the Battery
4) all are correct
5) none are correct
battery?
1)
2)
3)
ConcepTest 17.1
Which is the correct way to
light the lightbulb with the
Connect the Battery
4) all are correct
5) none are correct
battery?
1)
2)
3)
Current can only flow if there is a continuous connection from
the negative terminal through the bulb to the positive terminal.
This is only the case for Fig. (3).
Series Circuits
•
Electric current has but a single pathway through the circuit. This means that the current passing
through each electrical device is the same.
•
This current is resisted by the resistance of the first device, the resistance of the second, and that
of the third also, so the total resistance to current in the circuit is the sum of the individual
resistances along the circuit path.
•
The current in the circuit is numerically equal to the voltage supplied by the source divided by the
total resistance of the circuit. This is in accord with Ohm's law.
•
Ohm's law also applies separately to each device. The voltage drop, or potential difference,
across each device is proportional to its resistance. This follows from the fact that more energy is
used to move a unit of charge through a large resistance than through a small resistance.
•
The total voltage impressed across a series circuit divides among the individual electrical devices
in the circuit so that the sum of the voltage drops across each individual device is equal to the
total voltage supplied by the source.
Series Circuits 2
• Series Connections:
• Total Resistance = Sum of individual
Resistances. Rs  R1  R2  R3
Current the same through every load.
Example Series
Given: Three bulb s with the resistances R1=4Ω, R2=6 Ω, R3=12Ω, are
connected in series with a 6 V battery. Required to find:
a) The equivalent resistance of the bulbs Rs
Rs  R1  R2  R3
RS  4  6  12  22
b) The current flowing through each bulb
I
V
6V

 0.273 A
Rs 22
c) The voltage drop across each bulb:
V  IR 
V1  0.273 A  4  1.10V
V2  0.273 A  6  1.63V
V3  0.273 A  12  3.27V
d) The power dissipated by each bulb:
P  IV 
P1  (0.273 A)  1.1V  0.30W
P2  (0.273 A)  1.63V  0.45W
P3  (0.273 A)  3.27V  0.90W
Parallel Circuits
•
Each device connects the same two points A and B of the circuit. The voltage is therefore the
same across each device.
•
The total current in the circuit divides among the parallel branches. Since the voltage across each
branch is the same, the amount of current in each branch is inversely proportional to the
resistance of the branch—Ohm's law applies separately to each branch.
•
The total current in the circuit equals the sum of the currents in its parallel branches.
•
As the number of parallel branches is increased, the overall resistance of the circuit is decreased.
Overall resistance is lowered with each added path between any two points of the circuit. This
means the overall resistance of the circuit is less than the resistance of any one of the branches.
Parallel Connection
• Different parts of an electric circuit are
on separate branches.
Voltage: the same
Total current:
sum of currents in
each branch.
Resistance:
1
1
1
1
 

 ...
RP R1 R2 R3
Example Parallel
Given: Three bulb s with the resistances R1=4Ω, R2=6 Ω, R3=12Ω, are
connected in parallel with a 6 V battery. Required to find:
a) The equivalent resistance of the bulbs Rp
1
1
1
1
 

RP R1 R2 R3
1
1
1
1
3  2 1




RP 4 6 12
12
RP  2
b) The current flowing through each bulb and the total current:
I
V 6V

 1.5 A
R1 4
I
V
6V

 1A
R2 6
I
V
6V
V
6V

 0. 5 A I 

 3A
R3 12
R p 2
c) The voltage drop across each bulb:
V  IR 
V1  1.5 A  4  6V
V2  1A  6  6V
V3  0.5 A  12  6V
d) The power dissipated by each bulb:
P  VI 
P1  6V  1.5 A  9W
P2  6V  1.0 A  6W
P3  6V  0.5 A  3W
ConcepTest 18.1a
Series Resistors I
1) 12 V
Assume that the voltage of the battery
is 9 V and that the three resistors are
identical. What is the potential
difference across each resistor?
2) zero
3) 3 V
4) 4 V
5) you need to know the
actual value of R
9V
ConcepTest 18.1a
Series Resistors I
1) 12 V
Assume that the voltage of the battery
is 9 V and that the three resistors are
identical. What is the potential
difference across each resistor?
2) zero
3) 3 V
4) 4 V
5) you need to know the
actual value of R
Since the resistors are all equal,
the voltage will drop evenly
across the 3 resistors, with 1/3 of
9 V across each one. So we get a
3 V drop across each.
9V
Follow-up: What would be the potential difference if
R= 1 , 2 , 3  ?
ConcepTest 18.1b
Series Resistors II
1) 12 V
In the circuit below, what is the
2) zero
voltage across R1?
3) 6 V
4) 8 V
5) 4 V
R1= 4 
R2= 2 
12 V
ConcepTest 18.1b
Series Resistors II
1) 12 V
In the circuit below, what is the
2) zero
voltage across R1?
3) 6 V
4) 8 V
5) 4 V
The voltage drop across R1 has
to be twice as big as the drop
across R2. This means that V1 =
R1= 4 
R2= 2 
8 V and V2 = 4 V. Or else you
could find the current I = V/R =
(12 V)/(6 ) = 2 A, then use
12 V
Ohm’s Law to get voltages.
Follow-up: What happens if the voltage is doubled?
ConcepTest 18.2a
Parallel Resistors I
1) 10 A
In the circuit below, what is the
2) zero
current through R1?
3) 5 A
4) 2 A
5) 7 A
R2= 2 
R1= 5 
10 V
ConcepTest 18.2a
Parallel Resistors I
1) 10 A
In the circuit below, what is the
2) zero
current through R1?
3) 5 A
4) 2 A
5) 7 A
The voltage is the same (10 V) across each
R2= 2 
resistor because they are in parallel. Thus,
we can use Ohm’s Law, V1 = I1 R1 to find the
R1= 5 
current I1 = 2 A.
10 V
Follow-up: What is the total current through the battery?
•
Summary of Terms
Potential difference (synonymous with voltage difference) The difference in electric potential
between two points, measured in volts. When two points having different electric potential are
connected by a conductor, charge flows as long as a potential difference exists.
Electric current The flow of electric charge that transports energy from one place to another.
Measured in amperes, where 1 A is the flow of 6.25 × 1018 electrons per second, or 1 coulomb
per second.
Electrical resistance The property of a material that resists electric current. Measured in ohms
(Ω).
•
Ohm's law The statement that the current in a circuit varies in direct proportion to the potential
difference or voltage across the circuit and inversely with the circuit's resistance. A potential
difference of 1 V across a resistance of 1 Ω produces a current of 1 A.
Direct current (dc) Electrically charged particles flowing in one direction only.
Alternating current (ac) Electrically charged particles that repeatedly reverse direction, vibrating
about relatively fixed positions. In the United States the vibrational rate is 60 Hz.
Electric power The rate of energy transfer, or the rate of doing work; the amount of energy per
unit time, which electrically can be measured by the product of current and voltage. Measured in
watts (or kilowatts), where 1A × 1V = 1W.
•
Series circuit An electric circuit in which electrical devices are connected in such a way that the
same electric current exists in all of them.
•
Parallel circuit An electric circuit in which electrical devices are connected in such a way that the
same voltage acts across each one and any single one completes the circuit independently of all
the others.