Download Mechanical work vs. Electrical Discussion of Energy Hill Analogy for

Putting this together: Electric Force
Voltage and circuits
opposite charges attract
like charges repel
F
-
-
F
-
F
F
+
Consider 2 ‘point’ charges, A and B. What force does charge A feel?
qA
How are these the same thing?
Lecture 21 :
Electrical potential energy
Voltage
Starting Circuits.
+
-
---
-- +
- +
--
+
-
+
+
Wall at first
Remember force between charges = 𝒌
+ + +
𝒒𝑨 𝒒𝑩
𝒓𝟐
-
𝒒𝑨 𝒒𝑩
𝒓𝟐
Mechanical work vs. Electrical
-
Think, climbing up a hill
stores energy in system
-
Same thing, separating charges…
Polarized wall
Electrons are
repelled but can’t
get too far
• Electrons in balloon are then
ATTRACTED to the positive
charges
• They are REPELLED from the
negative ones.
• The repulsion is smaller because r
is bigger
Discussion of Energy
• 3 Types of energy (there are others):
Kinetic - energy of motion - rock rolling down hill
Potential - ability to do work in future - rock at the top of
a hill or a fluid has it under pressure.
Thermal - energy that dissipates as heat (e.g. friction, or
smashing into a wall)
• How would this apply to charges?
+
𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌
Reminders:
HW 9 due thursday
Reading for Tuesday:???
How does a charged particle attract a neutral one?
---
qB
• k is Coulomb constant = 9 x 109 N m2/C2
• qA and qB are amount of charge in coulombs (C )
• r is separation in m
• negative sign means attraction
Remember the balloon and the wall?
---
r
-
• Think of the analogy of a hill… pulling + away
from valley…
-
F
F
+
We just have to be more careful because unlike mass (all
masses attract each other) some charges attract while
others repel
Hill Analogy for energy
Effort (push) to get ball
(at constant speed):
up the hill
a) harder at first
b) easier at first
c) takes same effort / push
The force required is related to the steepness or
slope of the potential energy curve. Steeper
means more force.
1
Voltage
Hill Analogy for energy
Potential Energy of same ball
a
a) PEa > PEb
b
b) PEb > PEa
c) PEa = PEb
http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html
Voltage has to do with conditions of
system
• Amount of charge
• Distance from that charge
• Like the electric force (related but different)
Topo- practice
• Which figure
goes with #4
Voltage is like the height of
mountain
• Think Topographical maps
Voltage tells you what a + charge will do
+5V
-5V
+V is like top of hill
-V Is like valley
0V
• Answer C
Where is 0 V?
What will a +q do at 0V:
a) Be attracted to higher voltage
b) Be attracted to lower voltage
c) Not be impacted
b) Just like a ball rolls down hill
2
Voltage is like the height of
mountain
• Height (and gravity)
• Voltage
• Mass, m
• Charge, q
• Electrical Potential Energy • Gravitational
potential Energy
EPE = q D V
GPE = m g Dh
Electrostatic potential energy and voltage
New force: Electrostatic force between charges
New PE: Electric Potential Energy (EPE)
Forces and PE go in pairs - Remember gravitational force:
- Do work against gravitational force (mg) to raise an object’s GPE (mgh)
- Similarly, do work against electric force to raise an object’s EPE
EPE = q DV, where q = charge of object and DV is voltage difference
Like GPE with q  m and DV  gDh
Voltage (V)
- tells you EPE of any charge at that location in space
- Tells you work required to bring a unit charge from V = 0 to that location
- Determined by surrounding charges.
Closer you are to + charge the more + the voltage
- A grounded object is always at V = 0. Grounded means attached to the
ground!
- Always interested in DV: voltage difference between 2 locations
like GPE where only Dh mattered
Best understood by doing practice questions!
Two metal plates connected by a battery.
Battery maintains a voltage difference of V between the plates
Conservation of energy and EPE
Remember conservation of energy equation:
A
-
Work Done on object = Change in Energy of object
Wext - Wfriction = DPE + DKE
-
Now we can add another PE term to this equation:
q
++
-
V
+
+
+
+
+
+
B
V
Plate A-is grounded (set to zero V)
What is the voltage of plate B?
Wext - Wfriction = DGPE + DEPE + DKE
= mgDh + qDV + D(1/2mv2)
A
q +
+
+
+
+
+
++
a)
b)
c)
d)
B
0 +V
-V
- determine from information given
Can’t
q
A
++
-
-
V
+
+
+
+
+
+
B
EPE = qDV
-
What will happen to the charge q if we let go of it (ignore gravity)?
What is the change in EPE of charge as it flies from plate B to plate A?
a) Nothing
b) It will fly over to plate A
c) Sparks will fly
d) -Something else
a)
b)
c)
d)
0
+qV
-qV
Can’t determine
-
3
CT 29.4b
q
A
-
+
+
+
+
+
+
++
-
V
B
Conservation of energy:
Wext - Wfriction=
DGPE + DEPE + DKE
Did the electric potential energy (PE)
increase or decrease?
Did the voltage (V) at the position of the
test charge increase or decrease?
A: PE , V
C: PE ,
V
E: None of these.
Charged particle loses EPE as it flies from B to A.
What form has this energy turned into just before it hits plate A
a)
b)
c)
d)
A positive charge q is released from
position i to position f between the
charged plates.
-
B: PE , V
D: PE , V
KE
Thermal energy
GPEPPE
©University of Colorado, Boulder (2008)
CT 29.4
A negative charge -q is released from position i to position f
between the charged plates of a charged capacitor.
Electrostatics Summary
Did the potential energy (PE)
increase or decrease?
Did the voltage (V) at the position
of the test charge increase or
decrease?
• Positive and negative charge: Like charges repel, opposites attract
• Coulombs law for point charges: F = k qA qB
r2
Force acts along line joining particles
A: PE , V
B: PE , V
C: PE , V
D: PE , V
E: None of these.
• Voltage: Determines EPE of charge at that location in space
Close to + charges voltage is more + and vice versa
Grounded object is at 0V
Hint:
EPE = qDV
(Also called Electric Potential)
• EPE: = qDV
New form of potential energy
Lots of analogies to GPE (DVDh, qm)
©University of Colorado, Boulder (2008)
Flashlights, circuits, batteries, and power
light bulb circuit
+
+
=
• Given batteries, light bulbs, and wire, how can we design a light bulb circuit
a) that will burn brightest,
b) that will last longer,
c) that will be dim,
d) that will turn on and off.
• How can you control and predict current and power in light bulbs?
• All this basic circuit stuff applies to home wiring, home electronics, heaters etc.
• Thursday lecture … help save lives … physics of dangers of electrocution.
Builds on electrostatics (like charges repel, opposite charges attract, voltage, EPE)
………but now electrons are moving…………………
………. need to start thinking like an electron!
• Start by looking at a really simple circuit containing
- light bulb
- Battery
- Wires
• Each element made of metal containing
electrons that
are free to move
• What are the electrons doing in each
element to
ensure that the light bulb lights up?
+
Using each of these three elements can you draw a picture where the bulb lights up?
4
light bulb circuit: Wiring
See this in action!
What will happen when hook up positive end of battery (+) to
flashlight bulb with one wire?
a. light up b. barely light up c. not light up
-
+
http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc
Circuits so far
a.
b.
c.
d.
e.
Wires: Make complete circuit necessary for steady flow of
electrons
Usually have negligible (zero) resistance
Battery: Maintains a voltage difference DV between
terminals
Provides each electron with qDV = eV of EPE to
spend in circuit
Provides push for electrons around circuit (bigger
V, bigger push)
Bulb: Filament is a high resistance wire
KE of electrons converted into heat via
collisions
Electron rules for analyzing circuits
a) No electron deaths/births
b) No passing of electrons
c) Electrons have energy (high at start, low at end)
d) Different conducting materials have different resistances
Think like an electron!
a.
b.
c.
d.
e.
Light will not light up, No current will flow
Light will light up, Current will flow
Light will barely light up, Current will flow
Light will not light up, Current will flow
Light will light up, No current will flow.
Light will not light up, No current will flow
Light will light up, Current will flow
Light will barely light up, Current will flow
Light will not light up, Current will flow
Light will light up, No current will flow.
back to signal and battery applets for review as needed
Circuit language
Resistance (R) of a circuit element is measure of how hard
it is for electrons to pass through.
Units: Ohms (W)
What if increase voltage difference across battery?
a. Rate at which electrons pass through filament stays
the same
b. Rate at which electrons pass through filament
decreases
c. Rate at which electrons pass through filament
increases
Current (I) : charge per second flowing
past a point in the circuit
(= # electrons per second × charge on electron)
Units : Amps (1 A = 1 C/s)
Voltage (difference) (DV)
Vbatt
a) Across battery: Measure of EPE given to each e- as it passes through
battery. EPE given = eV. Related to pushing force on electrons in circuit
b) Across a resistor (wire, filament etc): Measure of EPE lost by each e- as it
passes through. EPE lost = eV.
Unless told otherwise voltage difference across connecting wire = 0.
Units: Volts (V)
Note: All quantities specific
to one component.
Ohm’s Law: DV = IR Resistance of component
Current through component Don’t mix and match!
Voltage dropped across component
5
Electrical Power
1.5A
If the battery on the left has a voltage
(difference) of 6V and it is pushing a current of
1.5 A through the bulb, what is the resistance of
9W
thea)
bulb?
b) 6 W
c) 4 W
d) 1.5 W
e) 0 W
What is the electrical power used up by each component in circuit?
POWER tells us how HOT something gets or how BRIGHT a bulb is
P = I DV
Don’t mix and match!
Voltage dropped across component
Current through component
Electrical power dissipated (used up) in component
Also Ohm’s Law: D V = IR
Substitute into power law to get different forms:
P = DV2/R
- I = V/R
- Useful if you know V and R but not I (parallel circuits)
6V
P = I2 R
- V = IR
- Useful if you know I and R but not V (series circuits)
P = I DV
- Useful if you know I and V but not R
Power question
I have a 60W bulb plugged into the mains.
Assume that the mains supply is like a 120V
battery
What current flows through the bulb?
a) 120A
b) 60A
c) 0.5A
d) 2A
e) 7200A
Power question
60W
I have a 60W bulb plugged into the mains.
Assume that the mains supply is like a 120V
battery
60W
What current flows through the bulb?
0.5A
120V
Batteries in series
Batteries provide a voltage difference between their terminals
If each battery below is an identical 3V battery, what is the total
voltage across the following arrangement?
a) 3V
b) 0V
c) 9V
d) 6V
e) Other
V
?
What is the resistance of the bulb filament?
a) 240 W
b) 2 W
c) 0.5 W
d) 30 W
e) Can’t determine
R
120V
Batteries in series (nose to tail)
case 1
Compare the brightness of the bulbs in case 1
and case 2.
All bulbs and batteries are identical
a.
b.
c.
d.
V
2 twice as bright as 1
2 same brightness but runs twice as long
2 much more than twice as bright as 1
2 produces no light
R
case 2
V
V
6
R
Batteries in parallel
case 1
a.
b.
c.
d.
V
R
R
Batteries in parallel
Compare the brightness of the bulbs in case 1
and case 2.
All bulbs and batteries are identical
2 twice as bright as 1
2 same brightness
2 much more than twice as bright as 1
2 produces no light
What is the difference then?
case 1
Each battery can produce a given
amount of
Current (electrons/ second) for a certain
amount of time
V
R
case 2
case 2
V
V
V
V
Note: rating on batteries is in AmpHours!
(what is an amp-hour?)
Zoinks.. All of a sudden, with two
batteries I have a greater reservoir of
electrons to draw from.
Case 2: last twice as a long!
R
V
V
Summary:
- Series: more energy for each electron!
(brighter)
how you make a 9 V out of D-Cells,
or AAAs
R
- Parallel: longer lasting
difference between AAAs and D cells
Car battery demo 1
Ohms Law (V=IR) and Power (P = I DV)
Connect paper clip across terminals.
What will happen?
a) nothing,
b) drain battery slightly,
c) melt paper clip,
d) melt wires,
e) both c. and d.
c)Melt paper clip.
How to figure out, how to explain?
When analyzing circuits – think like an electron!
V
V
Reasoning a little more mathematically
e
e
+
12 V
e
-
---------------
Melt paper clip.
How to figure out?
What current flows?
• Paperclip and wires are in series
 Same current through each
 R = Rpaperclip+Rwires (very small)
• I = DV/R
R small  I very big
Power from battery?
P = I DV
Where does this power go?
I large  P large
2
- Power used in wire = I Rwire
2
- Power used in paperclip = I Rclip
 Power used depends only on resistance of component
- Rpaperclip >> Rwire.
- More electrical power  heat in clip, so it melts. Wire not even hot.
This is how (old) fuses worked.
Car battery demo 2
Student volunteer grabs terminals with hands.
A. Nothing.
B. Will get zapped (flames etc.) like paperclip
C. will get mild jolt,
D. other
How to figure out? 1st step in process?
1. How much electrical power goes into person?
→ If a lot, zapped and flames, but if tiny, volunteer will not notice.
2. What determines amount of power through person?
P=DIV
Voltage (DV) set by battery =12V.
Current (I) = DV/R. Rperson is high, so for 12 V, I is very small.
 P is very small.
3. That’s the theory… how do we test?
Experiment……..
7
Avoiding electrocution- ohms law applied to the human body.
Avoiding electrocution- ohms law applied to the human body.
Extent of injuries are determined by 2 factors:
Extent of injuries are determined by 2 factors:
a) The amount of current that flows
b) Where it flows through the body
a) The amount of current that flows
b) Where it flows through the body
Rules of thumb:
• 1-5 mA you can barely feel
• 10 mA is painful
• 100 mA causes muscle contraction in the heart, can be lethal
Rules of thumb:
• 1-5 mA you can barely feel
• 10 mA is painful
• 100 mA causes muscle contraction in the heart, can be lethal
Resistance of dry skin ~105 ohms
Resistance of wet skin ~ 1000 ohms (but with wide variations)
Resistance of dry skin ~105 ohms
Resistance of wet skin ~ 1000 ohms (but with wide variations)
So: if 10,000 volts is applied briefly across a person’s dry chest, what happens?
a. no effect
b. sure electrocution without immediate treatment
c. painful but recover immediately
d. vaporize person
Don’t try this at home
Applying 120 volts between right arm and right foot
a. no effect
b. fibrillation and electrocution
c. painful but probably no significant damage
So: if 100 volts is applied briefly across a person’s dry chest, what happens?
a. no effect
b. sure electrocution without immediate treatment
c. painful but recover immediately
d. vaporize person
Don’t try this at home
120 V
Applying 120 volts to wet left hand,
right hand in pocket and wearing
rubber sole shoes
a. little effect
b. fibrillation and electrocution
c. painful but probably no significant
damage
Don’t try this at home
120 V
Applying 120V between wet left
hand and wet feet
a. little effect
b. fibrillation and electrocution
c. painful but probably no
significant damage
8