Transcript Current and Resistance Powerpoint

Current Electricity
11.1 Electric Current
Circuit – continuous conducting path between
terminals of a battery (or other source of EMF)
Electric Current – flow of charge (electrons)
I – current (amperes)
Q
I
Q – charge (coulomb)

t
T – time
11.1 Electric Current
Ampere (for Andre’ Ampere)
1A  1
C
s
Usually called an amp
Open Circuit – break in the
circuit, no current flow
11.1 Electric Current
Short Circuit – when the load is bypassed
Current increase
Ground – allows for a
continuous path for charge
flow
11.1 Electric Current
For historical reasons, current is defined as
being in the direction that positive charge
flows
11.1 Electric Current
11.2 Current and Drift Speed
Drift Speed – average distance that an
electron moves in a
given time period
For an electron in a copper
wire
0.0246m / s
11.2 Current and Drift Speed
11.3 Resistance and Ohm’s Law
George Simon Ohm
I V
The actual values depend on
the resistance of the conductor
IR  V
Called Ohm’s Law
R – resistance measured in Ohms (W)
11.3 Resistance and Ohm’s Law
Only true for Ohmic materials
Vacuum Tubes, Transistors, Diodes are
nonohmic
11.3 Resistance and Ohm’s Law
A graph of current vs. potential difference
The metallic conductor is ohmic
The diode and filament are not
11.3 Resistance and Ohm’s Law
Resistor – anything that uses
electric energy
Resistor – device used to control
current
The symbol for a resistor is
11.3 Resistance and Ohm’s Law
The resistance value of a resistor is indicated
by the colored bands on the resistor
11.3 Resistance and Ohm’s Law
Misconceptions
1. Cells (batteries) do not put out a constant
current. They maintain a constant
potential difference.
2. Current passes through a wire and
depends on the resistance of the wire.
Voltage is across the ends of the wire.
3. Current is not a vector, it is always parallel
to the conductor. The direction is from + to
-.
11.3 Resistance and Ohm’s Law
Misconceptions
4. Current or charge do not increase or
decrease. The amount of charge in one
end of the wire comes out of the other end.
11.3 Resistance and Ohm’s Law
11.4 Resistivity
Resistance is found to be directly proportional
to its length and inversely proportional to
its cross sectional area.
L
Rr
A
r is called the resistivity (Wm)
Longer extension cords must
be thicker to keep
resistance low
11.4 Resistivity
Some common resistivity values
Material
Silver
Copper
Gold
Aluminum
Tungsten
Platinum
Nichrome
Resistivity Temperature
Coefficient
(Wm)
(Co-1)
1.59x10-8 0.0061
1.68x10-8 0.0068
2.44x10-8 0.0034
2.65x10-8 0.00429
5.6x10-8 0.0045
10.6x10-8 0.00651
100x10-8 0.0009
11.4 Resistivity
Best Conductor is Silver, but Copper is close
and much cheaper
Tungsten is used in filaments
Nichrome
Apparently an Anime character
11.4 Resistivity
11.5 Superconductors
An element or compound that conducts
electricity without resistance
Become insulators above a critical
temperature
Uses
MagLev Trains
11.5 Superconductors
11.6 Electrical Energy and Power
The rate of energy flow for an electric circuit
W qV q
P

 V
t
t
t
That is more commonly written as
P  IV
Combining with Ohm’s Law it can also be
written
2
PI R
2
V
P
R
11.6 Electrical Energy and Power
The power company charges by the kilowatthour (kWh)
1kWh  (1000W )(3600s)  3,600,000 J
Just a cool picture
11.6 Electrical Energy and Power
Household circuits – wires will heat up as
current increases
In a 20A household circuit
P  IV  (20 A)(120V )  2400W
In a 15A household circuit
P  IV  (15 A)(120V )  1800W
Circuits are typically designed to run at 80% of
the rated power output
Different circuits have different gauge wires
(diameter)
11.6 Electrical Energy and Power
Circuit Breakers and Fuses
Break the circuit
11.6 Electrical Energy and Power
11.7 Sources of EMF
EMF – electromotive force – the potential
difference between the terminals of a source
when no current flows to an external circuit (e)
11.7 Sources of EMF
A battery will have an internal resistance (r)
So there is a potential drop due to the current
that travels through the cell
Vc  Ir
So the actual potential across the terminals of
a cell will be
V  E  Ir
This is called the terminal
voltage
11.7 Sources of EMF
11.8 Resistors in Series
When resistors are place in a single pathway
They are said to be in
series
A schematic would look
like this
11.7 Sources of EMF
The current in a series circuit is the same
throughout the circuit
IT  I1  I 2  ....I n
The potential across the source of EMF is
equal to the sum of the potential drops across
the resistors
VT  V1  V2  ....Vn
11.7 Sources of EMF
Since potential can be defined as
V  IR
We can rewrite the equation for potential as
I T ReqRVeqT I1V
R11 VIR22R2....
....
V
....
Rn nI n Rn
11.7 Sources of EMF
11.9 Resistors in Parallel
When resistors are place
in a multiple pathways
They are said to be in parallel
A schematic would look like this
11.9 Resistors in Parallel
The potential difference in a parallel circuit is
the same throughout the circuit
VT  V1  V2  ....Vn
The current through the source of EMF is
equal to the sum of the current through the
resistors
IT  I1  I 2  ....I n
11.9 Resistors in Parallel
Since current can be defined as
V
I
R
We can rewrite the equation for potential as
V1n
V1T V11 V12
IT  I1 I 2  ....I n
Req R1 R2
Rn
11.9 Resistors in Parallel
Circuits that contain both series and parallel
components need to be solved in pieces
This circuit contains
20W resistors in series
25W resistors and load series to each
other and parallel to the 40W
resistor
11.9 Resistors in Parallel
11.10 Kirchhoff’s Rules
Circuits that are a little more complex
We must use Kirchhoff’s rules
Gustov Kirchhoff
They are applications of the
laws of conservation of
energy and conservation
of charge
11.10 Kirchhoff’s Rules
Junction Rule – conservation of charge
At any junction, the sum of the currents
entering the junction must equal the sum of all
the currents leaving the junction
I1  I 2  I 3
11.10 Kirchhoff’s Rules
Loop Rule – the sum of the changes in
potential around any closed pathway of a
circuit must be zero
For loop 1
5V  5I1  2 I 3  3V  0
11.10 Kirchhoff’s Rules
Steps
I1
I3
I2
1. Label the current in each separate branch
with a different subscript (the direction does
not matter, if the direction is wrong, the
answer will have a negative value)
2. Identify the unknowns and apply V=IR
3. Apply the junction rule (at a in our case) so
that each current is in at least one equation
I1  I 2  I 3  0
11.10 Kirchhoff’s Rules
Steps
I1
I3
I2
4. Choose a loop direction (clockwise or
counterclockwise)
5. Apply the loop rule (again enough equations
to include all the currents)
a. For a resistor apply Ohm’s law – the value
is positive if it goes in the direction of the loop
b. For a battery, the value is positive if the
loop goes from – to + (nub to big end)
11.10 Kirchhoff’s Rules
Steps
I1
I3
I2
We’ll do the two inside loops
E1  I1R1  I 3R4  E3  I1R2  0
E3  I 3 R4  I 2R3  E2  0
6. Combine the equations and solve
11.10 Kirchhoff’s Rules
11.11 RC Circuits
Used
windshield wipers
timing of traffic lights
camera flashes
When the switch is closed
current flows and
potential difference
across the capacitor
increases
11.11 RC Circuits
Eventually the potential difference across the
capacitor is equal to the EMF of the battery
Current is now zero
11.11 RC Circuits
The shape of the curve is given by

Vc  e 1  e
t
RC

RC = the time constant
Measures how quickly the capacitor becomes
charged
All circuits have some resistance, so they all
take time to charge
11.11 RC Circuits