The study of electric charges in motion Electric Current
Jan 21, 2016
The study of electric charges in motion
Electric Current
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
6 ( 1 ) 0totalq q q q
A6q
B-1q
C0q
5totalq q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere A and B touch?
C0q
A6q
B-1qB2.5q
A2.5q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere B and C touch?
B2.5q
A2.5q
C0qC1.25q
B1.25q
Example: Charge Distribution cont.
• What is the total charge of three conducting spheres
A2.5q
C1.25q
B1.25q
2.5 1.25 1.25totalq q q q
5totalq q
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 variable Unit
I current A (amp)
1 1Cs A
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)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Time (s)
Cu
rren
t (A
)
Alternating Current (AC)• AC stands for alternating current. Here current switches
directions at a set frequency.
Current vs. Time (AC)
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4
Time (s)
Cu
rren
t (A
)
• AC stands for alternating current. Here current switches directions at a set frequency.
Alternating Current (AC)
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.
Voltage Source
OFF ON
1 1 JCV
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.
Resistor
Switch
Wire Battery
Voltmeter
Ammeter
A Conductor of Current
Opens and Closes Circuits
Provides Resistance to Current Flow
Source of DC Charge Flow
Measures Current
Measures Voltage
More Circuit Symbols• Here are some additional circuit symbols that you may see.
Potentiometer
AC Source
Ground
Crossing
Junction
Capacitor DiodeStores Charge on Plates
Variable Resistor
Provides AC Current
Drains Excess Charge Buildup
Only Allows Current to Flow One Way
All Four Wires Connect
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 ).
Ohm’s Law• The current in a circuit is directly proportional to voltage
and inversely proportional to resistance.
• This relationship is known as Ohm’s Law.
VR
I
Resistance ()
Voltage (V)
Current (A)
I V 1 I
R
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
RI
120
3.0
VR
A
40R
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.
• 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.
P VI 2P I R
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?
How can energy loss be reduced?
Either reduce I or R
R is a fix physical property
2
2
2( )*.2 / (3.5 )
1.4
41 (1.4 )
R wires km km
R
P I R
P A
2350p W
P VI
High voltage lines transmit power between 500,000V-750,000V to reduce energy loss. 2350
750,000
WI
V
.0031I A
2(.0031 ) (1.4 )lossP A
51.34 10lossP x W
2350
Original loss
P W
Sample Problem (Electrical Power)• What is the power consumed when the toaster in on for
45s ?
P VI 120 3.0P V A360P W
EP E Pt
t
360 45E W s
16,200E J
120V V3.0I A
Given
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:
• The amount of kilowatt-hours gets multiplied times a rate to find the overall energy cost.
E Pt kWh
Power (kW) Time (h)
C RECost ($)
Rate $kWh
Energy (kWh)
1kW =1000W
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?
1 1000 1000 JskW W
1 3600h sE Pt
1000 3600JsE s
3,600,000E J 63.6 10E J or
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?
C RE
1.2 240E kW h288E kWh
8 30 240t h h
$0.11 288kWhC kWh$31.68C
1200 1.2W kW
Example: Charge Distribution cont.
• Sphere B is twice as large as sphere A, what will be the charge distribution after they touch?
A5q
B5q
A3.33q
B6.67q
Electric Circuit & Energy Conversion Video Clip
Electron flow & Current video clip