Transcript Electric Current & Resistance

AP Physics
Chapter 17
Electric Current and Resistance
Chapter 17: Electric Potential, Energy,
and Capacitance
17.1
17.2
17.3
17.4
Batteries and Direct Current
Current and Drift Velocity
Resistance and Ohm’s Law
Electric Power
Homework for Chapter 17
• Read Chapter 17
• HW 17.A: p.562: 6-9, 12-17.
• HW 17.B: p. 562-563: 23-25; 28-34.
• HW 17.C: p. 564: 53-56; 60-64.
Warmup: Plugged In
Daily Physics Warmup # 104
Electrical appliances can be found in practically every room of most homes in the modern
world. They help us store and prepare food, provide entertainment, and allow us to
live in a comfortable environment. What all of these appliances have in common is that
they convert electrical energy into some other form of energy.
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Fill in the blanks to identify four of the types of energy produced in electrical appliances.
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17.1: Batteries and Direct Current
battery
- a device that converts chemical potential energy into
electrical energy.
• Allesandro Volta constructed one of the first practical batteries.
• He used zinc and copper electrodes in a weak sulfuric acid solution.
circuit
- any complete loop consisting of wires and electrical devices
ex: batteries and light bulbs.
anode
(+) - the positive terminal of a battery.
cathode
(-) - the negative terminal of a battery.
electric current
- the net rate at which charge flows past a given point.
direct current (dc)
- in a battery circuit, the electrons can only flow in
one direction, from negative terminal to positive terminal.
A Simple Chemical Battery: A battery consists of two electrodes (different metal strips)
in an electrolyte (solution that conducts electricity).
• The different metals dissolve at different rates in
the acid. As the metals dissolve, their atoms move
into solution as positively charged ions, leaving
behind electrons.
• Both electrodes accumulate excess electrons, but
one will have a larger excess.The cathode
becomes more negatively charged than the anode.
The anode is at a higher potential than the cathode.
•The potential difference across the electrodes can
cause electrons to flow in the wire. In other words,
the voltage causes current, or flow of charge, in the
wire. There is also a current in the solution as the
positive ions migrate, so the circuit is complete.
• Over time, as electrode A continues to receive more electrons than normal, it attracts
A ions from solution. A ions reattach to electrons to form neutral atoms and deposit on
the A electrode. In the mean time, B is slowly dissolving. The chemical potential energy
is converted to light and heat in the lightbulb.
electromotive force (emf)
- the potential difference across the two
terminals of a battery (or any dc power supply) when not connected to an
external circuit.
• emf is NOT a force; it is a voltage, measured in volts.
terminal voltage
- is the voltage across a battery or power
supply when it is connected to an external circuit.
• Also called operating voltage
• Terminal voltage is always less than the emf because of internal
resistance of the battery.
• A battery’s internal resistance depends on its age,
type of electrolyte, and electrode material.
• The terminal voltage is what a battery actual
delivers; it can be considerably less than the emf.
V =  - Ir
(add to your gold sheet)
terminal voltage = emf – (current) x (internal resistance of the battery)
Example: A battery has an emf of 8.40 V and an internal resistance of 0.5 .
It can supply a current of 0.084 A. What is its terminal voltage?
V =  - Ir
= 8.40 V – (0.084 A) (0.5)
= 8.36 V
Batteries in Series
• Notice the symbol for battery and
resistance. A resistance is
anything in the circuit that
opposes the charge flow.
• When batteries are connected in
series, their voltages add and the
voltage across the resistance R is
the sum of the voltages.
• Example: Car batteries. These
generally consist of six 2-volt cells
connected in series.
Batteries in Parallel
• When batteries of the same
voltage are connected in
parallel, the voltage across the
resistance is the same, as if only
a single battery were present.
• In this arrangement, each
battery supplies a fraction of the
total current.
•Example: jumping your car. The
strong battery (low resistance)
delivers most of the current to
help the weak battery (high
resistance).
17.2 Current and Drift Velocity
complete circuit
- a battery or some other source connected to a
continuous conducting path
• To sustain electric current, a voltage source and a complete circuit is
required.
conventional current
- the direction
in which positive charge would move.
• This is the historical or conventional
way to analyze circuits
• In most materials (e.g., metals), the
actual current is carried by electrons
moving in the opposite direction to the
conventional current due to the fact
that electrons have negative charge.
electric current
(I) – the time rate of flow of net charge
I=q
t
current
On Gold Sheet
where q is the net charge that passes
through a cross-sectional area of a wire at a
given point in time t at a constant rate.
• the SI unit of current is coulomb/s (C/s) or ampere (A), or “amps” for short
• named after Andre Ampère (1775-1836), an early investigator of electrical and
magnetic phenomena
drift velocity
- the average velocity of the electron flow in a metal
wire.
• much smaller than the random velocities of the electrons themselves.
• drift velocity is approximately 1 mm/s
• drift velocity is opposite the direction of the electric field, towards the
positive terminal of the battery.
• The electric field, which is what pushes the charges in the wire, travels
down the wire at close to the speed of light (on the order of 108 m/s).
• This is why the current starts “instantly” in all parts of the circuit.
Example 17.1: If 3.0 x 1015 electrons flow through a section of a wire of diameter
2.0 mm in 4.0 s, what is the electric current in the wire?
Check for Understanding
1. When a battery is placed into a complete circuit, the voltage across its terminal
is its
a) emf
b) terminal voltage
c) power
d) all of these
Answer: b
2. As a battery gets old, its
a) emf increases
b) emf decreases
c) terminal voltage increases
d) terminal voltage decreases
Answer: d
Check for Understanding
3. When four 1.5 volt batteries are connected in parallel, the output voltage of the
combination is
a) 1.5 V
b) 3.0 V
c) 6.0 V
d) none of these
Answer: a
4. The unit of electrical current is
a) C
b) C/s
c) A
d) both b and c
Answer: d
Homework for Sections 17.1 & 17.2
HW 17.A: p.562: 6-9, 12-17.
Warmup: Lighter Electric Bills
Daily Physics Warmup # 79
Electric light bulbs come with various power ratings, such as 60 W and 100 W.
Since light bulbs are used to produce light, it might seem logical that all light
bulbs with the same power rating would produce the same amount of light.
However, the power rating refers to how much energy is being used each
second. Some of that energy is converted to heat as well as light and varies
significantly depending on the nature of the bulb.
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Incandescent bulbs produce a lot more heat than fluorescent bulbs and therefore
use more power to produce the same amount of light. The savings in cost to
operate fluorescent bulbs can be quite surprising. It typically costs about 0.007¢
per watt to operate something electrically for one hour. A 60 W incandescent bulb
and a 15 W fluorescent bulb give off the same amount of light. Calculate the
amount saved over a year’s time if they were used an average of 10 hours per
day.
Answer: $ 11.50
17.3 Resistance and Ohm’s Law
resistance (R)
R= V
I
- the ratio of the voltage to the resulting current
or
V = IR
Ohm’s Law
On Gold Sheet
• The SI unit of resistance is the volt per ampere (V/A) or ohm ().
ohmic
- a resistor is said to be ohmic if it has constant resistance.
• Not all materials are ohmic: example: lightbulbs, semiconductors
Example 17.2: A resistor with a resistance of 20  is connected to a 12-volt battery.
What is the current through the resistor?
Factors That Influence Resistance
• The major factors that influence resistance of a conductor of uniform crosssection are:
1) the type of material or the intrinsic resistive properties
2) its length (L)
3) its cross-sectional area (A)
4) its temperature (T)
Resistivity
()
• determined by the resistive properties of a
material (partly due to intrinsic atomic properties)
R=L
A
or
 = RA
L
On Gold Sheet
where R is resistance
• the SI unit of resistivity is the ohm-meter ( · m)
() – the inverse of resistivity
conductivity
=1

• the SI unit of conductivity is 1/ohm-meter [( ·m)-1]
Example 17.3: Calculate the current in a piece of 10.0 m long 22-gauge (the radius
is 0.321 mm) nichrome wire if it is connected to a source of 12.0 V. Assume the
temperature is 20°C.
Check for Understanding
1. The unit of resistance is the
a. V / A
b. A / V
c. W
d. V
Answer: a
2. For an ohmic resistor, current and resistance
a) vary with temperature
b) are directly proportional
c) are independent of voltage
d) none of these
Answer: d (ohmic resistors have constant resistance by definition)
Check for Understanding
3. If voltage (V) were plotted on the same graph versus current (I) for two ohmic
conductors with different resistances, how could you tell the less resistive one?
Answer: Since V = R I (y = mx) , the one with the smaller slope is less
resistive.
Check for Understanding
Homework for Section 17.3
HW 17.B: p. 562-563: 23-25; 28-34.
Warmup: Power Up!
Daily Physics Warmup #77
Power is the rate at which energy is used. When an appliance is labeled with a certain
power, such as 1,200 watt hair dryer, it means that during each second of operation
the dryer transforms 1,200 joules of energy from one type of energy into other types
of energy.
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Identify the type of energy that operates the appliance and the type or types of energy it
produces.
Device
toaster
Energy In
electrical
Energy Out
heat (light)
portable generator
chemical
electrical
electric dryer
electrical
heat
flashlight
Electrical or
chemical
light (heat)
17.4 Electric Power
P = W = UE = q V
t
t
t
and since I = q,
t
P= I V
On Gold Sheet
• The SI unit of power is the watt (W).
joule heat
– the thermal energy expended in a current-carrying resistor
• also known as I2R losses (“I squared R” losses)
• can be undesirable (ex: electrical transmission lines)
• can be the intended purposes (ex: hair dryers, toasters)
• heat = power  time (J/s  s = J)
kilowatt-hour
(kWh) – a unit of work (energy)
1 kWh = (1000 W)(3600 s) = ( 1000 J/s)(3600 s) = 3.6 x 106 J
Example : What amount of heat is generated in a 10  resistor that carries 0.3 A of
current for 3 minutes?
Example 17.5: What is the operating resistance of a 100 W household light bulb?
The operating line voltage of household electricity is 120 V.
Example 17.6: A computer, including its monitor, is rated at 300 W. Assuming the
power company charges 10 cents for each kilowatt-hour of electricity used and the
computer is on 8.0 hours per day, estimate the annual cost to operate the
computer.
Check for Understanding
1. Electric power has units of
a)
b)
c)
d)
A2·
J/s
V2/ 
all of these
Answer: d
2. If the voltage across an ohmic resistor is doubled, the power expended in the
resistor
a) increases by a factor of 2
b) increases by a factor of 4
c) decreases by half
d) none of these
Answer: b, since P=V2/R
Check for Understanding
3. If the current through an ohmic resistor is halved, the power expended in the
resistor
a) increases by a factor of 2
b) increases by a factor of 4
c) decreases by half
d) decreases by a factor of 4
Answer: d, because P = I2R
4. Assuming your hair dryer obeys Ohm’s law, what would happen if you plugged it
directly into a 240-volt outlet in Europe if it is designed to be used in the 120-volt
outlets of the US?
Answer: Since P = V2/R, its power output would quadruple, and it would
overheat at least.
Homework for Section 17.4
• HW 17.C: p. 564: 53-56; 60-64.
Chapter 17 Formulas
V =  - Ir
Defines terminal voltage in terms of emf, current, and internal
resistance of a battery.
I=q
t
Define electric current in terms of charge flow.
V = IR
Ohm’s Law.
R=L
A
Defines the resistivity of a material.
=1

Conductivity is the reciprocal of resistivity.
P = IV = I2R = V2
R
Computes the electric power delivery to a resistor.