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Electric Current
The study of electric charges in motion
Potential Difference (V)
• Charge flows from higher potential to lower
potential until electric potential equilibrium is
reached.
• When electric potential is zero (equilibrium),
current flow stops.
Example: Charge Distribution
• What is the total charge of three conducting spheres with
charges of 6q,-1q, and 0q
qtotal  6q  (1q)  0q
qtotal  5q
A
6q
B
-1q
C
0q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere A and B
touch?
A
6q
2.5q
B
-1q
2.5q
C
0q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere B and C
touch?
A
2.5q
B
1.25q
2.5q
C
0q
1.25q
Example: Charge Distribution cont.
• What is the total charge of three conducting spheres
qtotal  2.5q  1.25q  1.25q
qtotal  5q
A
2.5q
B
1.25q
C
1.25q
Electric Current
• Electrical charge in motion is electric current.
• Current is measured by counting the amount of
charges that pass a given point per second
Symbol
I
variable
current
Unit
A (amp)
1 Cs  1A
Comparing a DC circuit to Flow of
Water
http://faraday.physics.utoronto.ca/IYearLab/Intros/DCI/Flash/WaterAnalogy.html
•What component in the electrical circuit is equivalent
to the pump in the animation?
Direct Current (DC)
• DC stands for direct current. Here current only travels in
one direction.
Current vs. Time (DC)
1.2
Current (A)
1
0.8
0.6
0.4
0.2
0
0
1
2
Time (s)
3
4
Alternating Current (AC)
• AC stands for alternating current. Here current switches
directions at a set frequency.
Current vs. Time (AC)
1.5
Current (A)
1
0.5
0
-0.5
0
1
2
-1
-1.5
Time (s)
3
4
Alternating Current (AC)
• AC stands for alternating current. Here
current switches directions at a set
frequency.
Voltage
• Current flows only when there is a potential
difference (V)
• Voltage sources can sustain a potential difference
• Voltage in a circuit is analogous to pressure in a
water hose.
J
C
1V  1
OFF
ON
Voltage Source
Voltage Sources
• There are different types of devices that can provide a
source of voltage.
• Sources that provide DC include:
– Batteries
– DC Power Supplies
– DC Generators
• Sources that provide AC include:
– Electrical Outlets
– Alternators
– Power Inverters
Electric Circuits
• Electric current flows very well if there is a complete loop
for charge to flow. This is called an electrical circuit.
• Circuits often contain various elements, giving it practical
use. Examples of circuit elements include:
– Switches
– Sources of Resistance (Such as a Light)
– Meters
Circuit Symbols
• Each circuit element has its own symbol.
• Common circuit symbols are shown below.
Wire
Battery
A Conductor
of Current
Switch
Source of DC
Charge Flow
Ammeter
Opens and
Closes Circuits
Resistor
Measures
Current
Voltmeter
Provides Resistance
to Current Flow
Measures
Voltage
More Circuit Symbols
• Here are some additional circuit symbols that you may see.
Capacitor
Diode
Stores Charge
on Plates
Potentiometer
Variable
Resistor
Only Allows Current
to Flow One Way
Junction
All Four Wires
Connect
AC Source
Provides AC
Current
Ground
Drains Excess
Charge Buildup
Crossing
Wires Only Cross
and do not Connect.
Electrical Resistance
• Every circuit contains some resistance to current flow.
• This is due to imperfections in the crystalline lattice
structure of the conductor.
• Imagine the lattice structure below is the atoms in a wire.
• Notice how the moving electrons experience resistance.
• The variable for resistance is R.
• The unit for resistance is the Ohm (symbol W).
Ohm’s Law
• The current in a circuit is directly proportional to voltage
and inversely proportional to resistance.
1
I 
R
IV
• This relationship is known as Ohm’s Law.
Voltage (V)
V
R
I
Resistance (W)
Current (A)
Sample Problem (Ohm’s Law)
• A toaster is connected to a 120V outlet and draws 3A of
electrical current.
• What is the resistance of the toaster?
V
R
I
120V
R
3.0 A
R  40W
Power (Watt W)
Power measures the rate at which energy is
transferred.
• Thermal energy P=I2R
– Wasted or unwanted energy during
transmission
Power and Electricity
• There are also two useful equations that relate power to
electrical quantities.
P  VI
PI R
2
• Notice how current is squared in the second equation.
Increasing current in a circuit drastically increases the
power consumed.
• High current wires generate heat.
• This is why electricity transferred over large distances is
at high voltage and not high current. Otherwise, the
power losses would be very wasteful.
Resistance of power lines is .2 ohms per Km
How much power is lost during transmission
if a home 3.5Km from the power plant cooks
on a stove that draws 41A?
R  2( wires )*.2W / km(3.5km)
R  1.4W
P  I 2R
P  412 A(1.4W)
p  2350W
How can energy loss be
reduced?
Either reduce I or R
R is a fix physical property
P  VI
High voltage lines transmit
power between 500,000V750,000V to reduce energy
loss.
Original loss
P  2350W
2350W
I
750, 000V
I  .0031A
Ploss  (.0031A) 2 (1.4W)
5
Ploss  1.34 x10 W
Sample Problem (Electrical Power)
• What is the power consumed when the toaster in on for
45s ?
Given
V  120V
I  3.0 A
P  VI
P  120V  3.0 A
P  360W
E
P   E  Pt
t
E   360W  45s 
E  16, 200 J
The Kilowatt Hour
• Did you ever read an electric bill?
• You are charged for the number of kilowatt
hours used during the month.
• This is energy, not power, because:
E  Pt
1kW =1000W
kWh
Time (h)
Power (kW)
• The amount of kilowatt-hours gets
multiplied times a rate to find the overall
energy cost.
C  RE
Cost ($)
Rate
Energy (kWh)
 
$
kWh
How Much Energy is a kWh?
• We all know that the SI unit for energy is the Joule (J).
• How many Joules are there in one kilowatt hour?
1kW  1000W  1000 J s
1h  3600s
E  Pt
E  1000 J s  3600s 
E  3, 600, 000 J
or
E  3.6 10 J
6
Sample Problem (KWh)
• During the winter, an electric heater runs 8 hours every
day over the course of a month (30 days).
• The power consumed by the heater is 1200W.
• How many kWh of energy are consumed?
• If the rate is $0.11 per kWh, then what is the cost to
operate the heater?
1200W  1.2kW
t  8h  30  240h
E  1.2kW  240h 
E  288kWh
C  RE
$
C   0.11 kWh
  288kWh
C  $31.68
Example: Charge Distribution cont.
• Sphere B is twice as large as sphere A, what will be the
charge distribution after they touch?
A
5q
A
3.33q
B
5q
6.67q
Electric Circuit & Energy
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