1. Current and Resistance
Chapter 19
Current
and
Resistance

2. 19.1 Electric Current Objectives
Describe the basic properties of electric current
Solve problems relating current, charge and time
Distinguish between the drift speed of a charge carrier and the average speed of the charge carrier between collisions
Differentiate between direct current and alternating current

3. Where is electric current?
….wherever there is a net movement of electric charge through a medium.
Examples
In any electronic device
In our car engines
In our body

4. What is electric current?
…the rate at which electric charges move through a given area

5. Equation for Electric Current (I)
electric current = charge passing through a given area
time interval
units of current = ampere (A)
1A = 1 C/s

6. Current Example Problem
The amount of charge that passes through the
filament of a light bulb in 2.00s is 1.67C.
What is the current in the light bulb?
How many electrons pass through the filament
in the 2.00s time span?
I=0.835 A
N = 1.04x1019 electrons

7. “Conventional Current” Flow
…is defined in terms of positive
charge movement

8. Charge Movement Requires a good conductor Examples of good conductors?
Copper and other metals
Salt water and other electrolytes

9. Electron Motion in a Conductor
When you flip on a light switch, you
introduce an E-field that travels through
the wire at nearly the speed of light
(3.0x108 m/s).
But the electrons themselves do not
actually travel that fast….instead they travel
at a rate called the “drift velocity”.

10. Electrons collide with the metal atoms
as they flow through the conductor,
so they don’t follow a straight path
Notice direction of electron flow !!!

11. Drift Velocity
Is the net velocity of the charge carrier moving in an electric field
Because there are so many collisions as the electrons move in the electric field, drift velocity is very small, even though E is moving VERY fast (about the speed of light)

12. Where does current come from??
Create a condition of unequal potential energy across a conductor
The current flows from higher electric potential (and PE) to lower electric potential (and PE)

13. Sources of Current When will the current stop moving?
Batteries: convert chemical energy into electrical energy
Generators : convert mechanical energy into electrical energy
When will the current stop moving?

14. Types of Current
Direct current (DC) – charges move only one direction because the terminals of the charge source always maintain the same sign (example: current flowing in a battery circuit)
Alternating current (AC) – charges move in both directions because the terminals of the charge source are constantly changing signs. There is no net motion of charge, they just vibrate back and forth (example: current in your house)

15. DC: constant voltage
AC: voltage flip flops
between + and -
time

16. Questions
A 3.0 C charge passes through the filament of a light bulb in 5.00 s.
a) What is the current?
b) How many electrons pass thru the bulb in 1.0 min?
a) 0.60 A
b) 2.25x1020 electrons
The compressor on an air conditioner draws 40.0 A when it starts up. If the start-up time is 0.5 s, how much charge passes in that time?
ans: 20 C

17. 19.2 Resistance Objectives
Calculate the resistance, current and potential difference using the definition of resistance
Distinguish between ohmic and non-ohmic materials
Know what factors affect resistance
Describe what is unique about superconductors

18. What is resistance?
….the impedance of motion of charge through a conductor.

19. Which battery can provide more current to a light bulb, a 9V or a 12V?
All things being equal, the 12V battery would
provide more current. But the current provided
to the bulb by the battery also depends on the
connecting wires and the bulb’s filament etc.
These other features in the circuit
that impede current flow comprise
the circuit’s resistance.

20. R = ΔV I The resistance to current flow is:
Resistance = potential difference
current
units of resistance = ohms (Ω)

21. Ohm’s Law I In other words: ΔV = IR
The resistance is constant over a wide range of potential differences (for most materials)
In equation form, Ohm’s Law is:
ΔV = constant (R) I
In other words: ΔV = IR

22. More on Ohm’s Law It is NOT a fundamental law of nature
It is NOT true for all materials
Ohmic materials do follow Ohm’s Law and have a constant resistance over a wide range of ΔV’s
Non-ohmic materials are those whose resistance can vary over a range of ΔV’s

23. Ohmic materials Non-ohmic materials * ΔV vs I is straight line graph
* Slope of graph = I/ΔV = 1/R
Non-ohmic materials
* ΔV vs I is not linear

24. A material’s resistance depends on:
Length: the longer the item, the greater it’s resistance
Cross-sectional area: small cross sections (thin wires) offer more resistance than thick wires
Material: the type of material affects the resistance (Al has higher resistance than Cu)
Temperature: the higher the temperature the higher the resistance

25. Why are resistors needed?
…to control current across a conductor.
Consider your household voltage:
* The voltage is constant at the outlet
* Some appliances cannot handle the
amount of current that is available
in the wire (based on voltage and wire size)
* Resistors are used in the appliances to
limit the current that they see

26. Superconductors
Materials that have no resistance below a critical temperature
Once a current is established in them, the current continues even if the potential difference source is removed!!

27. Questions How much current would a 10.2 ohm toaster
draw when attached to a 120 V outlet?
Ans: 12 A
2. An ammeter registers 2.5 A of current in a
wire that is connected to a 9.0 V battery.
What is the wire’s resistance?
Ans: 3.6 ohms

28. About batteries……

30. Cathode: Gives electrons, Anode: Gets electrons
(thus becomes positive)
Anode:
Gets electrons
(thus becomes negative)

31. What’s happening in a simple circuit?
Chemical energy stored in the battery
is converted to the electrical energy
of the charge carriers
2. The charge move from one battery terminal
through the wire, which has very little
resistance (because it’s a good conductor)
3. The charge gets to the light bulb, which
has higher resistance. In the light bulb
the charge loses electrical potential energy
due to collisions. The PEelec is converted
to internal energy, and the light bulb
filament heats up, causing the glow.
4. The charge returns to the other battery
terminal with zero potential energy. As the
charge moves back across the battery to
the other terminal, the battery does work on
the charge and the charge gains PEelec.

32. 19.3 Electric Power Objectives
Relate electric power to the rate at which electrical energy is converted to other forms of energy
Calculate electric power
Calculate the cost of running electrical appliances

33. Electrical Power
…..the rate at which the charge carriers do work.
Aka: the rate at which the charge carriers convert electrical potential energy to non-electrical forms of energy.

34. Equations for Power P = W = ΔPE Δt Δt Δt
Power is the rate at which work is done
P = W = ΔPE
Δt Δt
Since ΔPE = qΔV, then P = qΔV Δt
But from 19.1 we know I = q Δt

35. P = IΔV P = I2R So that leaves us with…..
units of P (power) is watts (W)

36. Electric Power Usage Power companies charge for ENERGY
usage, not POWER (watts) usage
Instead of charging for each watt (or
kilowatt) you use, they charge for each
kilowatt you use for each hour you use it
ENERGY usage and electrical billing is based
on kilowatt-hours

37. Kilowatt-hour vs Joules
kW-hr and J are both units of energy
1 kW-hr x 103 W x 60 min x 60 sec = 3.6 x 106 W-sec
1 kW hr min
And 1 W-sec = 1 J
So, 1 kW-hr = 3.6 x 106 J

38. Why High Voltage in Power Lines?
Recall that P=I2R, and this is the rate at
which charge carriers lose potential energy
(they lose potential energy because the
potential energy is being converted to
another form of energy)
So, the energy loss across any resistor
is proportional to the resistance and the
square of the current. To reduce this
energy loss, you can either reduce
resistance (R), or reduce current (I).
Since P=IΔV, as you reduce current (I) you must also increase
voltage (ΔV) in order to transmit the same amount of power.

39. Power to Your Home High voltage lines from the power plant transmit
at voltages as high as
765,000 V
Transformers are used
to step down the voltage
to ~ 4,000 V within the city
Transformers are used
again to step down the
voltage to your home to
120 V

40. Questions 1. The operating potential difference of a light
bulb is 120 V. The power rating of the bulb
is 75 W.
a) What is the current in the bulb?
b) What is the bulb’s resistance?
2. A steam iron draws 6.0 A when plugged into
a 120 V outlet.
a) What is the power rating of this iron?
b) How many joules of energy are
produced in 20.0 min?
c) How much does it cost to run the
iron for 20.0 min at $0.010 per kW-hr

41. Answers
1. a) A
b) 190 Ω
2. a) 720 W
b) 8.6x105 J
c) $0.0024

42. Circuit Fluid Model In the water analogy, water flowed because
there was a difference in gravitational potential
energy between the full tank and the empty tank.
In a circuit, the battery provides the potential
difference that “pushes” the charges to flow.
The wires are the pipes the charges flow
through. A lamp or resistor would be like a
water wheel in a water circuit.