Current and Resistance

1
Chapter 17

• Current and Resistance

2
Electric Current

• Whenever electric charges of like signs move, an
  electric current is said to exist
• The current is the rate at which the charge flows
  through this surface
• Look at the charges flowing perpendicularly to a
  surface of area A
• The SI unit of current is Ampere (A)
• 1 A 1 C/s

3
Electric Current, cont

• The direction of the current is the direction
  positive charge would flow
• This is known as conventional current direction
• In a common conductor, such as copper, the
  current is due to the motion of the negatively
  charged electrons
• It is common to refer to a moving charge as a
  mobile charge carrier
• A charge carrier can be positive or negative

4
Properties of a Current
5
Definition of a Current
6
Conservation of Current
7
Checking Understanding

• Rank the bulbs in the following circuit according
  to their brightness, from brightest to dimmest.
• A ? B ? C ? D
• A ? B ? C ? D
• A ? D ? B ? C
• B ? C ? A ? D

8
Answer

• Rank the bulbs in the following circuit according
  to their brightness, from brightest to dimmest.
• A ? B ? C ? D
• A ? B ? C ? D
• A ? D ? B ? C
• B ? C ? A ? D

9
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

10
Meters in a Circuit Voltmeter

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

11
Resistance

• In a conductor, the voltage applied across the
  ends of the conductor is proportional to the
  current through the conductor
• The constant of proportionality is the resistance
  of the conductor

12
Resistance, cont

• 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

13
Georg Simon Ohm

• 1787 1854
• Formulated the concept of resistance
• Discovered the proportionality between current
  and voltages

14
Ohms Law

• Experiments show that for many materials,
  including most metals, the resistance remains
  constant over a wide range of applied voltages or
  currents
• This statement has become known as Ohms Law
• ?V I R
• Ohms Law is an empirical relationship that is
  valid only for certain materials
• Materials that obey Ohms Law are said to be ohmic

15
Ohms Law, cont

• An ohmic device
• The resistance is constant over a wide range of
  voltages
• The relationship between current and voltage is
  linear
• The slope is related to the resistance

16
Ohms Law, final

• Non-ohmic materials are those whose resistance
  changes with voltage or current
• The current-voltage relationship is nonlinear
• A diode is a common example of a non-ohmic device

17
Reading Quiz

• The charge carriers in metals are
• electrons.
• positrons.
• protons.
• a mix of protons and electrons.

18
Answer

• The charge carriers in metals are
• electrons.
• positrons.
• protons.
• a mix of protons and electrons.

Slide 22-7
19
Reading Quiz

• A battery is connected to a resistor. Increasing
  the resistance of the resistor will
• increase the current in the circuit.
• decrease the current in the circuit.
• not affect the current in the circuit.

20
Answer

• A battery is connected to a resistor. Increasing
  the resistance of the resistor will
• increase the current in the circuit.
• decrease the current in the circuit.
• not affect the current in the circuit.

21
Reading Quiz

• A battery is connected to a resistor. As charge
  flows, the chemical energy of the battery is
  dissipated as
• current.
• voltage.
• charge.
• thermal energy.

22
Answer

• A battery is connected to a resistor. As charge
  flows, the chemical energy of the battery is
  dissipated as
• current.
• voltage.
• charge.
• thermal energy.

23
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

24
Resistivity
The resistance of a wire depends on its
dimensions and the resistivity of its material
Slide 22-22
25
Temperature Variation of Resistivity

• For most metals, resistivity increases with
  increasing temperature
• With a higher temperature, the metals
  constituent atoms vibrate with increasing
  amplitude
• The electrons find it more difficult to pass
  through the atoms

26
Temperature Variation of Resistivity, cont

• For most metals, resistivity increases
  approximately linearly with temperature over a
  limited temperature range
• ? is the resistivity at some temperature T
• ?o is the resistivity at some reference
  temperature To
• To is usually taken to be 20 C
• ? is the temperature coefficient of resistivity

27
Temperature Variation of Resistance

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

28
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 as a normal metal above TC,
  but suddenly drops to zero at TC

29
Superconductors, cont

• The value of TC is sensitive to
• Chemical composition
• Pressure
• Crystalline structure
• Once a current is set up in a superconductor, it
  persists without any applied voltage
• Since R 0

30
Superconductor, final

• Good conductors do not necessarily exhibit
  superconductivity
• One application is superconducting magnets

31
Electrical Energy and Power

• In a circuit, as a charge moves through the
  battery, the electrical potential energy of the
  system is increased by ?Q?V
• The chemical potential energy of the battery
  decreases by the same amount
• As the charge moves through a resistor, it loses
  this potential energy during collisions with
  atoms in the resistor
• The temperature of the resistor will increase

32
Energy Transfer in the Circuit

• Consider the circuit shown
• Imagine a quantity of positive charge, DQ, moving
  around the circuit from point A back to point A

33
Energy Transfer in the Circuit, cont

• Point A is the reference point
• It is grounded and its potential is taken to be
  zero
• As the charge moves through the battery from A to
  B, the potential energy of the system increases
  by DQDV
• The chemical energy of the battery decreases by
  the same amount

34
Energy Transfer in the Circuit, final

• As the charge moves through the resistor, from C
  to D, it loses energy in collisions with the
  atoms of the resistor
• The energy is transferred to internal energy
• When the charge returns to A, the net result is
  that some chemical energy of the battery has been
  delivered to the resistor and caused its
  temperature to rise

35
Electrical Energy and Power, cont

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

36
Electrical Energy and Power, final

• The SI unit of power is Watt (W)
• I must be in Amperes, R in ohms and DV in Volts
• 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

37
Checking Understanding
The wires below carry currents as noted. Rate the
currents IA, IB and IC
38
Answer
The wires below carry currents as noted. Rate the
currents IA, IB and IC
39
Batteries
The potential difference between the terminals of
a battery, often called the terminal voltage, is
the batterys emf.
40
Simple Circuits
The current is determined by the potential
difference and the resistance of the wire
41
Checking Understanding

• A battery is connected to a wire, and makes a
  current in the wire. Which of the following
  changes would increase the current?
• Increasing the length of the wire (2) keeping
  the wire the same length, but making it thicker
  (3) using a battery with a higher-rated voltage
  (4) making the wire into a coil, but keeping its
  dimensions the same (5) increasing the
  temperature of the wire.
• All of the above
• 1 and 5
• 1, 4, and 5
• 2 and 3
• None of the above

42
Answer

• A battery is connected to a wire, and makes a
  current in the wire. Which of the following
  changes would increase the current?
• Increasing the length of the wire (2) keeping
  the wire the same length, but making it thicker
  (3) using a battery with a higher-rated voltage
  (4) making the wire into a coil, but keeping its
  dimensions the same (5) increasing the
  temperature of the wire.
• All of the above
• 1 and 5
• 1, 4, and 5
• 2 and 3
• None of the above

43
Checking Understanding Measuring Light Intensity

• A battery is connected to a photoresistor. When
  light shines on this resistor, it increases the
  number of charge carriers that are free to move
  in the resistor. Now, the room lights are turned
  off, so less light falls on the photoresistor.
  How does this affect the current in the circuit?
• The current increases.
• The current decreases.
• The current is not affected.

44
Answer

• A battery is connected to a photoresistor. When
  light shines on this resistor, it increases the
  number of charge carriers that are free to move
  in the resistor. Now, the room lights are turned
  off, so less light falls on the photoresistor.
  How does this affect the current in the circuit?
• The current increases.
• The current decreases.
• The current is not affected.

45
Power in Circuits
46
Energy and Power in Resistors
47
Checking Understanding

• A resistor is connected to a 3.0 V battery the
  power dissipated in the resistor is 1.0 W. The
  battery is traded for a 6.0 V battery. The power
  dissipated by the resistor is now
• 1.0 W
• 2.0 W
• 3.0 W
• 4.0 W

48
Answer

• A resistor is connected to a 3.0 V battery the
  power dissipated in the resistor is 1.0 W. The
  battery is traded for a 6.0 V battery. The power
  dissipated by the resistor is now
• 1.0 W
• 2.0 W
• 3.0 W
• 4.0 W

49
Summary
50
Additional Questions

• A set of lightbulbs have different rated voltage
  and power, as in the table below. Which one has
  the highest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

51
Answer

• A set of lightbulbs have different rated voltage
  and power, as in the table below. Which one has
  the highest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

52
Additional Questions

• 2. A set of lightbulbs have different rated
  voltage and power, as in the table below. Which
  one has lowest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

53
Answer

• 2. A set of lightbulbs have different rated
  voltage and power, as in the table below. Which
  one has lowest resistance?
• Bulb Rated voltage Rated power
• A 10 V 1 W
• B 8 V 1 W
• C 12 V 2 W
• D 6 V 2 W
• E 3 V 3 W

54
Additional Questions

• 3. A battery makes a circuit with a lightbulb as
  shown. Two compasses are near the wires before
  and after the bulb in the circuit. Which compass
  experiences a larger deflection?
• Compass 1 experiences a larger deflection.
• Compass 2 experiences a larger deflection.
• C. Both compasses experience the same deflection.

55
Answer

• 3. A battery makes a circuit with a lightbulb as
  shown. Two compasses are near the wires before
  and after the bulb in the circuit. Which compass
  experiences a larger deflection?
• Compass 1 experiences a larger deflection.
• Compass 2 experiences a larger deflection.
• C. Both compasses experience the same deflection.

56
Additional Questions

• 4. In Trial 1, a battery is connected to a single
  lightbulb and the brightness noted. Now, in Trial
  2, a second, identical, lightbulb is added. How
  does the brightness of these two bulbs compare to
  the brightness of the single bulb in Trial 1?
• The brightness is greater.
• The brightness is the same.
• The brightness is less.

57
Answer

• 4. In Trial 1, a battery is connected to a single
  lightbulb and the brightness noted. Now, in Trial
  2, a second, identical, lightbulb is added. How
  does the brightness of these two bulbs compare to
  the brightness of the single bulb in Trial 1?
• The brightness is greater.
• The brightness is the same.
• The brightness is less.

58
End of Chapter Problems
3, 12, 22, 28, 32, 35, 38, 39