Transcript Chapter 25: Voltage, Current, and Resistance

Chapter 25
Current, Resistance, and
Electromotive Force
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc. Modified 2016 Scott Hildreth – Chabot College
Goals for Chapter 25
• To understand current & how charges move in a
conductor
• To understand resistivity and conductivity
• To calculate resistance of a conductor
• To learn how an emf (E) causes current in a circuit
• To calculate energy & power in circuits
Current
• Current is any motion of charge
from one region to another.
• Current I = dQ/dt
[Amps]
• E field in conductor causes
charges to flow.
• E field created by Potential
Difference!
Direction of current flow
• A current can be produced by positive or negative charge flow.
• Conventional current is treated as a flow of positive charges.
• The moving charges in metals are electrons (see figure below).
Current, drift velocity, and current density
• Suppose:
– n charged particles/volume
– drift velocity vd
– time element dt
– Cross-sectional area A
• dQ = q (nAvd dt)
• I = dQ/dt = nqAvd (scalar)
• Define current density J
– J = I/A = nqvd (vector)
Current, drift velocity, and current density
• Example:
– 18 gauge wire
(diameter = 1.02 mm);
Current, drift velocity, and current density
• Example:
– 18 gauge wire
(diameter = 1.02 mm);
– current 1.67 A
–
200 Watt lamp
– Electron density = 8.5
x 1028/m3 .
• What is J and vd?
Resistivity
• Resistivity of material = ratio of E field in material to current
density it causes:  = E/J.
• Large  = LARGE field needed to generate small current!
Resistivity
• Conductivity is the reciprocal of the resistivity.
• High conductivity = large current results from small E field.
Resistivity and temperature
• Resistivity depends on temperature.
•
~ Linear R(T) = R0[1+a(T-T0)]
Resistance
• Resistance of conductor R = L/A [Ohms]
• Potential decreases across a conductor is V = IR
•
Going from higher V to lower; in direction of current
• V = IR (Ohm’s Law) … OR… I = V/R
Resistors are color-coded for easy identification
•
This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.
Ohmic and nonohmic resistors
• Only resistor in Figure (a) below obeys Ohm’s law.
Electromotive force and circuits
• An electromotive force (emf) makes current flow.
In spite of the name, an emf is not a force.
• “EMF” is a voltage difference!
•
Ideal source – EMF is constant
•
Vab = E
• For simple complete circuits,
EMF “pushes” + current around
from start to finish.
+
Electromotive force and circuits
EMF in an open circuit
(Battery not connected to
anything)
Electromotive force and circuits
EMF in an complete circuit
Internal resistance
• Real sources of emf actually
contain some internal
resistance r.
• The terminal voltage of an
emf source is Vab =  – Ir.
• Terminal voltage of 12-V
battery is less than 12 V
when actually connected to
the light bulb.
Symbols for circuit diagrams
Example 25.4 – OPEN circuit
• EMF = 12 V; internal r = 2 Ohms (very large!!!)
• Not connected to anything (yet)
• What do ideal Voltmeter and Ammeter read?
Source in a complete circuit
• Now add a 4-Ohm resistor to the same source….
• What is total resistance? What is current? Vab?
Source in a complete circuit
• Now add a 4-Ohm resistor to the same source….
• Total resistance of SERIES resistors = 2 + 4 = 6 Ohms
Source in a complete circuit
Vab:
12V – (2A x 2W) = 8V
Va’b’ = IR
2A x 4W = 8V
Ideal I =
12V/6 W
=2A
Using voltmeters and ammeters
What do Ammeters and Voltmeters do to circuits?
Using voltmeters and ammeters
What do Ammeters and Voltmeters do to circuits?
Ammeters measure
flow of current PAST a
point.
Ideally, they should
NOT influence the
current
Ideally, R(ammeter) = 0!
Put them IN SERIES
with circuit “legs”
Using voltmeters and ammeters
What do Ammeters and Voltmeters do to circuits?
Voltmeters measure
pressure difference
across (or between)
points in the circuit.
Ideally, they should
NOT influence the
current
Ideally, R(voltmeter) = !
Put them in parallel!
Using voltmeters and ammeters
What do Ammeters and Voltmeters do to circuits?
Using voltmeters and ammeters
What do Ammeters and Voltmeters do to circuits?
Voltmeter in Series!
R(voltmeter) = 
No current will flow!
A source with a short circuit
• Without a resistor, what happens?
Potential changes around a circuit
• “Loop Rule”:
– NET change in
potential = zero
for “round trip” in a
circuit
• Net EMF for a loop
equals sum of voltage
“drops” across resistors
and/or other elements.
Energy and power in electric circuits
• Rate energy is delivered to
(or extracted from) a circuit
element is P = VabI.
•
[POWER] = [WATTS]
• Power delivered to pure resistor:
P = I2R = Vab2/R.
Energy and power in electric circuits
• Rate energy is delivered to (or
extracted from) a circuit element
is P = VabI.
•
[POWER] = [WATTS]
• Power delivered to pure resistor:
P = I2R = Vab2/R.
Power input and output
•
What are rates of energy conversion and power dissipation in circuit?
Power input and output
•
What are rates of energy conversion and power dissipation in circuit?
–
Battery provides EI = 12 V x 2A = 24 Watts
–
Energy dissipation in battery = I2r = 8 Watts
–
Energy dissipation in 4W resistor = 16 Watts
Power in a short circuit
• Short Circuit bypasses resistance, allowing charge to flow
without “obstruction”
Remove
this!
Power in a short circuit
• Now power = 12 V x 6A = 72 W = I2R(internal)
Theory of metallic conduction
• Random motion of
electrons in a conductor.
PGE Rates & Meanings….
• PGE Home rates (3/16):
• What’s a KWh??
PGE Rates & Meanings….
• What’s a KWh??
•
Kilowatt = 1000 Watts = 1000 Joules/Second
•
Kilowatt-hour = 1000 Watts x 3600 seconds
•
= 3.6 x 106 Joules = 3.6 MegaJoules
•
= 3.6 MJ
• How much energy do I use?
•
100W light bulb 5 hours at night to study physics?
•
0.1 KW x 5 hours = 0.5 KWh @ $.18/KWh
•
Only 9 CENTS!!! (See!! Study physics more!)
What do we use on average in the US?
~ 911 KWh/residence/month2 (electricity)
~
12,000 KWh/year
~ 80K – 90K KWh (80- 90 MWh) of energy
from all sources per person per year1
Sources:
1 US Department of Energy [Internet]. How much electricity does an American home use? 2012
Oct 3. http://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3
2 Energy in the United States. (2016, March 7). In Wikipedia, The Free Encyclopedia. Retrieved
March 7, 2016, from
https://en.wikipedia.org/w/index.php?title=Energy_in_the_United_States&oldid=708828662