Current and Resistance

1
Chapter 17

• Current and Resistance

Conceptual questions 3,6,10,14 Quick quizzes
1,3,4,5,6,7 Problems 12,27,30,47
2
Electric Current

• The current is the rate at which the charge flows
  through a surface
• The direction of current flow is the direction
  positive charge would flow
• The SI unit of current is Ampere (A)
• 1 A 1 C/s

3
Consider positive and negative charges moving
horizontally through the four regions in Figure
17.2. Rank the currents in these four regions,
from lowest to highest.
QUICK QUIZ 17.1
4
Charge Carrier Motion in a Conductor

• The zig-zag black line represents the motion of
  charge carrier in a conductor
• The net drift speed is small
• The sharp changes in direction are due to
  collisions
• The net motion of electrons is opposite the
  direction of the electric field

5
Electrons in a Circuit

• The drift speed is much smaller than the average
  speed between collisions
• Although the drift speed is on the order of 10-4
  m/s the effect of the electric field is felt on
  the order of 108 m/s

6
Meters in a Circuit -- Ammeter

• An ammeter is used to measure current
• In line with the bulb, all the charge passing
  through the bulb also must pass through the meter

7
Meters in a Circuit -- Voltmeter

• A voltmeter is used to measure voltage (potential
  difference)
• Connects to the two ends of the bulb

8
Look at the four circuits shown below and
select those that will light the bulb.
QUICK QUIZ 17.3
9
Resistance

• The resistance of the conductor
• Units of resistance are ohms (O)
• 1 O 1 V / A
• Resistance in a circuit arises due to collisions
  between the electrons carrying the current with
  the fixed atoms inside the conductor

10
Ohms Law ohmic materials ?V I R

• Ohms Law is an empirical relationship
• Materials that obey Ohms Law are said to be ohmic

11
Non-ohmic materials

• The current-voltage relationship is nonlinear
• A diode is a common example of a non-ohmic device

12
In the figure below, does the resistance of the
diode (a) increase or (b) decrease as the
positive voltage ?V increases?
QUICK QUIZ 17.4
13
Resistivity

• The resistance of an ohmic conductor is
  proportional to its length, L, and inversely
  proportional to its cross-sectional area, A
• ? is the constant of proportionality and is
  called the resistivity of the material
• See table 17.1

14
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15
Problem 17-12

• Suppose that you wish to fabricate a uniform wire
  out of 1 g of copper. If the wire is to have a
  resistance of R0.500 Q, and if all of the copper
  is to be used, what will be
• A. the length
• B. the diameter of that wire?

16
Aliens with strange powers visited Earth and
doubled every linear dimension of every object on
the surface of the Earth. A wire has the length
and diameter twice their original values. Does
the wire now have (a) more resistance than
before, (b) less resistance, (c) the same
resistance? (Assume the resistivities of
materials remain the same before and after the
doubling.)
QUICK QUIZ 17.5
17
Temperature Variation of Resistivity

• For most metals, resistivity increases
  approximately linearly with temperature
• ?o is the resistivity at some reference
  temperature To
• To is usually taken to be 20 C
• ? is the temperature coefficient of resistivity
• see Table 17.1

18
Temperature Variation of Resistance

• Since the resistance of a conductor with uniform
  cross sectional area is proportional to the
  resistivity, the effect of temperature on
  resistance is

19
Problem 17-27

• A 34.5 m length of copper wire at 20.0oC has a
  radius of 0.25 mm. If a potential difference of
  9.0 V is applied across the length of the wire,
  determine the current in the wire.
• If the wire is heated to 30.0oC while the
  potential difference is maintained, what is the
  resulting current in the wire?

20
Problem 17-30
A platinum resistance thermometer has resistances
of 200.0 O when placed in a 0C ice bath and
253.8 O when immersed in a crucible containing
melting potassium. What is the melting point of
potassium? (Hint First determine the resistance
of the platinum resistance thermometer at room
temperature, 20C.)
The resistance at 20.0C is Solving
for T gives the
temperature of the melting potassium as
21
Superconductors

• A class of materials and compounds whose
  resistances fall to virtually zero below a
  certain temperature, TC
• TC is called the critical temperature
• The graph is the same above TC, but suddenly
  drops to zero at TC

22
Electrical Energy and Power

• The rate at which the energy is lost is the power
• From Ohms Law, alternate forms of power are

23
Electrical Energy and Power

• The SI unit of power is Watt (W)
• The unit of energy used by electric companies is
  the kilowatt-hour
• This is defined in terms of the unit of power and
  the amount of time it is supplied
• 1 kWh 3.60 x 106 J

24
A voltage ?V is applied across the ends of a
nichrome heater wire having a cross-sectional
area A and length L. The same voltage is applied
across the ends of a second heater wire having a
cross-sectional area A and length 2L. Which wire
gets hotter? (a) the shorter wire, (b) the
longer wire, (c) not enough information to say.
QUICK QUIZ 17.6
25
For the two resistors shown here, rank the
currents at points a through f, from largest to
smallest.
QUICK QUIZ 17.7
26
Problem 17-47
The heating coil of a hot water heater has a
resistance of 20 W and operates at 210 V. If
electrical energy costs 0.080/kWh, what does it
cost to raise the 200 kg of water in the tank
from 15 C to 80 C?
The kilowatt-hour is a measure of energy equal
to The energy needed to raise the temperature of
200 kg of water from 15 C to 80 C is and
the cost of operating the heater to produce this
quantity of thermal energy is (cost) (energy
used) (rate) (15 kWh) (0.080/kWh) 1.20
27
Conceptual questions

• Why dont the free electrons in a metal fall to
  the bottom of the metal due to gravity? Charges
  in a conductor are suppose to reside on the
  surface why dont the free electrons all go to
  the surface?
• 6. Two lightbulbs are each connected to a voltage
  of 120V. One has a power of 25 W, the other 100
  W. Which bulb has a higher resistance? Which
  bulb carries more current?
• 10. Some homes have light dimmers that operate by
  rotating a knob. What is being changed in the
  electric circuit when the know is being rotated?
• 14. Use the atomic theory of matter to explain
  why the resistance of a metal should increase as
  its temperature increases.

28
In the two cases shown here a battery is
connected up to a box containing some resistors.
The battery provides an EMF V0. Which box will
draw more current from the battery? 1. They will
draw the same amount. 2. 1 will draw twice as
much as 2. 3. 1 will draw more than 2 but not
twice. 4. 2 will draw twice as much as 1 5. 2
will draw more than 1 but not twice. 6. You
cant tell from the information given
29
MCAT

• A positive charge q1.1x10-11 C is located 0.01 m
  away from a negative charge of equal magnitude.
  Point P is exactly between them. What is the
  magnitude of the electric field at point P?
• a. 1000 N/C b. 2000 N/C
• c. 4000 N/C d. 8000 N/C
• If a water molecule is placed between two plates
  of a capacitor, which orientation would it take
  to minimize its energy? The electric field is
  up.
• a. H b. H
• O O
• H H
• c. H H d. O
• O H H

E
30
MCAT, cont.

• The ratio of the potential difference across a
  conductor and the current moving through it is
  called the
• a. resistance b. capacitance
• d. conductance d. electric potential
• In a solid metal conductor, electric current is
  the movement of
• a. electrons only b. protons only
• c. nuclei d. protons and electrons
• A 12 W load is connected across a 6.0 V battery.
  How much energy does the load use in ½ an hour?
• a. 1.5 x 10-3 kWh b. 2.0 x 10-3 kWh
• c. 3.0 x 10-3 kWh d. 12 x 10-3 kWh