Download Chapters 18 and 19

Chapter 18
Electric Currents
18.1 The Electric Battery
First battery –
consisted of two
dissimilar metals
connected by a
conductive solution
called an electrolyte.
The Electric Battery
• A battery transforms chemical energy
into electrical energy.
• Chemical reactions within the cell (or
solar energy) create a potential
difference between the terminals
• Called the “Electro Motive Force” or
EMF (ε)
• Not really a force, unit is the volt
Moving Charges = current
Conductor
+
+
+
+
Chuck E Cheese
wrist watch
Current = (amount of charge going by)/(time)
18.2 Electric Current
Electric current is the rate of flow of charge
through a conductor:
(18-1)
Unit of electric current: the ampere (Amp), A.
1 A = 1 C/s.
Electric Circuit Components
+
ε
Battery
-
Capacitor
C
R
Resistor
18.2 Electric Current
In order for current to flow, there must be a
path from one battery terminal, through the
circuit, and back to the other battery
terminal. Only one of these circuits will work:
18.2 Electric Current
By convention, current is defined as flowing
from + to -. Electrons actually flow in the
opposite direction, but not all currents consist
of electrons.
18.3 Ohm’s Law: Resistance and
Resistors
Experimentally, it is found that the current in
a wire is proportional to the potential
difference between its ends:
18.3 Ohm’s Law: Resistance and
Resistors
The ratio of voltage to current is called the
resistance:
(18-2a)
(18-2b)
18.3 Ohm’s Law: Resistance and
Resistors
In many conductors, the
resistance is independent
of the voltage; this
relationship is called
Ohm’s law. Materials that
do not follow Ohm’s law
are called nonohmic.
Unit of resistance: the ohm, Ω.
1 Ω = 1 V/A.
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.
18.4 Resistivity
The resistance of a wire is directly
proportional to its length and inversely
proportional to its cross-sectional area:
The constant ρ, the resistivity, is
characteristic of the material.
18.4 Resistivity
18.4 Resistivity
For any given material, the resistivity changes
with temperature:
Since
R T  R 0 1   T - T0 
R0 = Resistance at some reference temperature (T0)
α = temperature coefficient and R = resistance
at some new temperature T
If  positive, if T , R 
If  negative if T , R 
Semiconductors are complex materials, and
may have resistivities that decrease with
temperature.
18.4 Resistivity
18.8 Microscopic View of Electric Current
When a potential difference is applied across a
conductor, the electrons acquire an average
drift velocity (vd) as they move through the
medium, colliding with imperfections, atomic
motions, etc..
Volume = LxA and L = vd x Δt
Length = L
Area = A
18.8 Microscopic View of Electric Current
This drift speed is related to the current in the wire,
and also to the number of electrons per unit volume
(n) which depends on the material.
Q (within region)  Number of Charges x
Charge of each one
Q  n(Volume)( e)
 nAv d t(e)
I
j   nev d
A
Length = L
Area = A
V (voltage)
E = V/L
Macroscopic
Quantities
R
Microscopic
Quantities
ρ
Relationship
V
E
V=EL
I
j = n e vd
I=jA
L
R ρ
A
18.5 Electric Power
Power, as in kinematics, is the energy
transformed by a device per unit time:
18.5 Electric Power
The unit of power is the watt, W.
1Watt = 1 Joule/second
Power
•
•
•
•
•
Power = Energy/time
Unit = 1 watt = 1J/s
You are billed for electrical energy use
E = (P)(t) = kw-hr
100 W light bulb for one day
E  (100 watts)(24 hrs)(3600 s/hr)
 8.6 10 J  2000 kcal
6
Heat
• Unit = kcal (heat required to raise 1
kg of water 10 C)
• 1 kcal = 4.18 x 103 J (Food Calorie)
18.7 Alternating Current
Current from a battery
flows steadily in one
direction (direct current,
DC). Current from a
power plant varies
sinusoidally (alternating
current, AC).
18.7 Alternating Current
The voltage varies sinusoidally with time:
as does the current:
(18-7)
18.7 Alternating Current
Multiplying the current and the voltage gives
the power:
18.7 Alternating Current
Usually we are interested in the average power:
18.7 Alternating Current
The current and voltage both have average
values of zero, so we square them, take the
average, then take the square root, yielding the
root mean square (rms) value.
(18-8a)
(18-8b)
18.9 Superconductivity
In general, resistivity decreases as temperature
decreases. Some materials, however, have
resistivity that falls abruptly to zero at a very low
temperature, called the critical temperature, TC.
18.9 Superconductivity
Experiments have shown that currents, once
started, can flow through these materials for
years without decreasing even without a
potential difference.
Critical temperatures are low; for many years no
material was found to be superconducting above
23 K.
More recently, novel materials have been found
to be superconducting below 90 K, and work on
higher temperature superconductors is
continuing.
Summary of Chapter 18
• Ohmic materials have constant resistance,
independent of voltage.
• Resistance is determined by shape and
material:
• ρ is the resistivity.
Summary of Chapter 18
• Power in an electric circuit:
• Direct current is constant
• Alternating current varies sinusoidally
Summary of Chapter 18
• The average (rms) current and voltage:
• Relation between drift speed and current:
Chapter 19
DC Circuits
Conservation Laws
• Conservation of Charge (I = Q/t) and I
• Conservation of Energy (PE = QV) and
V
• Conservative Forces (pages 148-149)
• ∑ of Work around a closed path = 0
• Independent of Path
• For a closed loop ∑ of PE gained and
lost or ∑ of V gained and lost = 0
Conservation Laws
I
ε
+
-
R
Conservation of Charge (I = Q/t) and I
I out of battery = I into resistor = I out of resistor
= I into battery
Conservation of Energy (PE = QV) and V
Analogy
Baseballs
Heavy oil
Person does work to lift baseballs, they gain energy
Baseballs fall through heavy oil and loose energy
Oil heats up.
Energy in = energy out
I
ε
+ VH
- VL
VA
R
VB
Battery does work and energy increases by Qε
Where ε = (VH - VL)
As charge goes through resistor energy is lost
(QV) where V = VA - VB
Qε - QV = 0
ε=V
I
ε
+
-
ε-V = 0
ε –IR =0
ε = IR
Simple Circuit
R
V = IR
Simple Circuits
I
R1
ε
+
R2
ε – IR1 – IR2 = 0
ε – I(R1 + R2)= 0
ε= V1 + V2
EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
a and b are the
terminals of the
battery
I
Going around circuit
ε – Ir – IR = 0
a
r
ε
R
+
b
Va - Vb = ε - Ir
EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current – these are called sources of
emf.
Battery is a nearly constant voltage source, but
does have a small internal resistance, which
reduces the actual voltage from the ideal emf:
(19-1)
Resistors in Series
A series connection has a single path from
the battery, through each circuit element in
turn, then back to the battery.
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.
(19-2)
V = V1 + V2 + V3
V = IR1 + IR2 + IR3= IReq
Resistors in Series
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit).
Resistors in Parallel
A parallel connection splits the current; the
voltage across each resistor is the same:
∑ V around closed path = 0
Independent of Path
V = I1R1
V = I2R2
V = I3R3
Resistors in Parallel
The total current is the sum of the currents
across each resistor:
Resistors in Parallel
This gives the reciprocal of the equivalent
resistance:
(19-4)
Repeat this Mantra
• The current is the same for
elements connected in series
• The voltage is the same for
elements connected in parallel
Light Bulbs
Rated by Power across 120 volts
Examples: 50 watts @ 120 volts;
100 watts @ 120 volts
Which has higher resistance?
2
2
V
V
P  IV  I R 
; R
R
P
2

120 volts 
For 50 W bulb R 
2
 288 
50 W
2

120 volts 
For 100 W bulb R 
 144 
100 W
Resistors in Series and in Parallel
What is Equivalent Resistance?
1
1
1
3



6Ω 3Ω R EQ 6Ω
R EQ  2Ω
R EQ  4Ω  2Ω  6Ω
Resistors in Series and in Parallel
What is Current through the 6Ω Resistor?
From (c) I = 3A and V across 6Ω resistor = 18V
I through 4Ω and 2Ω resistors = 3A
V across 6Ω and 3Ω resistors = 6V
19.3 Kirchhoff’s Rules
Some circuits cannot be broken down into
series and parallel connections.
Multiple Loop Game Rules
• Draw picture
• Define number of loops
• Pick ARBITRARY directions for the
currents
• Indentify branch points (where currents
divide)
• Currents into branch points = currents out
of branch points
• Circle each loop and ∑ V’s = 0
How to circle a loop
• Start at some ARBITRARY point
• Circle clockwise or counterclockwise (your
choice)
• End at starting point
How to Add V’s
When you come to
a Battery as you circle
the loop
ε
-ε
Direction you take
+ε
When you come to
a Resistor as you circle
the loop you will travel
with or against the
current
R
I
- IR
+ IR
19.4 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
19.4 EMFs in Series and in Parallel;
Charging a Battery
EMFs in series, opposite direction: total
voltage is the difference, but the lowervoltage battery is charged.
19.4 EMFs in Series and in Parallel;
Charging a Battery
EMFs in parallel only make sense if the
voltages are the same; this arrangement can
produce more current than a single emf.
19.5 Circuits Containing Capacitors in
Series and in Parallel
Capacitors in
parallel have the
same voltage across
each one:
19.5 Circuits Containing Capacitors in
Series and in Parallel
In this case, the total capacitance is the sum:
(19-5)
19.5 Circuits Containing Capacitors in
Series and in Parallel
Capacitors in series have the same charge:
19.5 Circuits Containing Capacitors in
Series and in Parallel
In this case, the reciprocals of the
capacitances add to give the reciprocal of the
equivalent capacitance:
(19-6)
19.6 RC Circuits – Resistor and Capacitor
in Series
When the switch is closed, the capacitor will
begin to charge.
19.6 RC Circuits – Resistor and Capacitor
in Series
The voltage across the capacitor increases
with time:
This is a type of exponential.
19.6 RC Circuits – Resistor and Capacitor
in Series
The charge follows a similar curve:
This curve has a characteristic time constant:
(19-7)
19.6 RC Circuits – Resistor and Capacitor
in Series
If an isolated charged capacitor is connected
across a resistor, it discharges:
19.7 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!
18.6 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.
18.6 Power in Household Circuits
Fuses are one-use items – if they blow, the
fuse is destroyed and must be replaced.
18.6 Power in Household Circuits
Circuit breakers, which are now much more
common in homes than they once were, are
switches that will open if the current is too
high; they can then be reset.
19.7 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.
19.7 Electric Hazards
A person receiving a
shock has become part
of a complete circuit.
2 prongs vs. 3 prongs
19.7 Electric Hazards
Faulty wiring and improper grounding can be
hazardous. Make sure electrical work is done by
a professional.
19.8 Ammeters and Voltmeters
An ammeter measures current; a voltmeter
measures voltage. Both are based on
galvanometers, unless they are digital.
The current in a circuit passes through the
ammeter; the ammeter should have low
resistance so as not to affect the current.
19.8 Ammeters and Voltmeters
A voltmeter should not affect the voltage across
the circuit element it is measuring; therefore its
resistance should be very large.
19.8 Ammeters and Voltmeters
An ohmmeter measures
resistance; it requires a
battery to provide a
current
I want to measure Current and
Voltages in this Circuit without
disturbing the Circuit
I use Ammeters
and Voltmeters
Ammeters – Very small resistance
so voltage across it is very small
In series
Voltmeters - Very large resistance, takes away
little current.
In Parallel
What would happen if I put an
Ammeter in Parallel?
A
Summary of Chapter 19
• A source of emf transforms energy from
some other form to electrical energy
• A battery is a source of emf in parallel with an
internal resistance
• Resistors in series:
Summary of Chapter 19
• Resistors in parallel:
• Kirchhoff’s rules:
1. sum of currents entering a junction
equals sum of currents leaving it
2. total potential difference around closed
loop is zero
Summary of Chapter 19
• Capacitors in parallel:
• Capacitors in series:
Summary of Chapter 19
• RC circuit has a characteristic time constant:
• To avoid shocks, don’t allow your body to
become part of a complete circuit
• Ammeter: measures current
• Voltmeter: measures voltage