1. ELECTRIC CURRENT
Chapter 23:

2. Flow of Charge
When there is a potential difference—charge flows from one end to the other. The flow of charge persists for as long as there is a potential difference.
Water flow.

3. Electric Current Electric Current: steady flow of electric charge.
In circuits of metal wires, electrons make up the flow of charge
Convention: current has the direction of the flow of positive charges.

4. Definition of CurrentI
Current (I) =amount of charge that passes through a cross sectional area of a conductor in one unit of time.
Charge
Charge
Time
I =
Unit of measurement:
Cross-sectional area
Ampere (A)

5. Unit of Current
The rate of electrical flow is measured in amperes. One ampere is a rate of flow equal to 1 coulomb of charge per second. (Recall that 1 coulomb, the standard unit of charge, is the electric charge of 6.25 billion billion electrons.)
In a wire that carries 5 amperes, for example, 5 coulombs of charge pass any cross section in the wire each second.
In a wire that carries 10 amperes, twice as many electrons pass any cross section each second.

6. Electric Current Example
How many electrons flow through a cross sectional area of a conductor in 5s, if it is traveled by a current of 3.2 A
1. Find the total charge:
2. Find the number of electrons N using the charge of an electron e=1.6 x 10-19C

7. Current (continuation)
Source: converts other forms of energy into electric energy.
Flow of “+” charge
Low
High A B
Potential
Potential
Source

8. Analogy
A ball rolling down a hill
High
Low
Difference of height causes the ball to roll down the hill.

9. Sources
High Potential
Low Potential
Batteries (Voltage sources):
Purpose is to provide a constant potential difference (voltage) between two points. + - V OR

10. Sources
Electromagnetic induction: conversion of electromagnetic energy into electricity.
Piezoelectric: mechanical stress on certain crystals creates a difference of potential.
Photoelectric effect: light energy is converted into electric energy.
Batteries: convert chemical energy into electric energy.

11. Voltage A useful meter is a multimeter, which
can measure voltage or current, and sometimes resistance.
To measure voltage, the meter’s probes are touched to two places in a circuit or across a battery.

12. Measuring current
If you want to measure current you must force the current to pass through the meter.
Multimeters can measure two types of current: alternating current (AC) and direct current (DC).

13. Resistance
Resistance (R): opposition to the flow of the electric current. Caused by collisions b/w electrons and the atoms of the metal.
Measured in ohms Ω.
Depends upon type of material (resistivity), proportional to length, inversely proportional to thickness (cross sectional area A).

14. Resistance
Increase the length, flow of electrons impeded (more collisions)
Increase the cross sectional area, flow facilitated (more space)
The structure of this relation is identical to heat flow through materials … think of a window for an intuitive example
How thick?
How big?
What’s it made of? or 14

15. Resistance Continuation
R is proportional to the temperature. At low temperatures conductors exhibit low resistance (superconductors).
Causes electric energy to turn into heat.

16. Electric Circuit
Electric Circuit: complete path through which a current can flow. Made of a source of current (battery), connecting wires, and an electricity user.
User
Wires I S

17. Simple Electric Circuit Analogy

19. Electric Circuits
When drawing a circuit diagram, symbols are used to represent each part of the circuit.

20. Electrical Symbols
Electrical symbols are quicker and easier to draw than realistic pictures of the components.

22. Ohm’s Law
Determined experimentally the relationship between current and voltage in a circuit.

23. Ohm’s Law A R S Source: provides electric energy.
I=V/R V A R S
Source: provides electric energy.
V - voltmeter: measures voltage (parallel)
A - ammeter: measures electric current (series)

24. Ohm’s Law Examples
For a given circuit of constant resistance, current and voltage are proportional to each other. This means we'll get twice the current for twice the voltage. The greater the voltage, the greater the current. But if the resistance is doubled for a circuit, the current will be half what it would be otherwise. The greater the resistance, the smaller the current.
Ohm's law tells us that a potential difference of 1 volt established across a circuit that has a resistance of 1 ohm will produce a current of 1 ampere.
If 12 volts are impressed across the same circuit, the current will be 12 amperes.
The resistance of a typical lamp cord is much less than 1 ohm, while a typical light bulb has a resistance of more than 100 ohms. An iron or electric toaster has a resistance of 15–20 ohms. Inside electrical devices such as radio and television receivers, current is regulated by circuit elements called resistors, whose resistance may be a few ohms or millions of ohms.

25. Examples Numerical
1. How much current will flow through a lamp that has a resistance of 60 Ω when 12 V are impressed across it?
2. What is the resistance of an electric frying pan that draws 12 A when connected to a 120-V circuit?

26. Ohm's Law and Electric Shock
The damaging effects of shock are the result of current (not voltage!) passing through the body.
The resistance of one's body depends on its condition and ranges from about 100 ohms if soaked with salt water to about 500,000 ohms if the skin is very dry.
If we touch the two electrodes of a battery with dry fingers, completing the circuit from one hand to the other, we can expect to offer a resistance of about 100,000 ohms. We usually cannot feel the current produced by 12 volts, and 24 volts just barely tingles. If our skin is moist, 24 volts can be quite uncomfortable.
Effect of Electric Currents on the Body 
Current (A)
Effect
0.001
Can be felt
0.005
Is painful
0.010
Causes involuntary muscle contractions (spasms)
0.015
Causes loss of muscle control
0.070
If through the heart, serious disruption; probably fatal if current lasts for more than 1 s
1. At a resistance of 100,000 Ω, what will be the current in your body if you touch the terminals of a 12-volt battery? 2. If your skin is very moist—so that your resistance is only 1000 Ω—and you touch the terminals of a 12-volt battery, how much current do you receive? A
0.012 A

27. Direct Current and Alternating Current
direct current (dc): the charges are flowing in one direction.
Alternating current (ac) charges are flowing first in one direction and then in the opposite direction. The current changes direction constantly at a given frequency.

28. Drift Velocity
The motion of the electrons cased by the electric field is affected by collisions with the atoms the metal is made of.
Therefore, the velocity in the direction of the field along the wire called drift velocity is extremely low (hundredth of a centimeter per second).
Electric Field

29. Electric Power
The rate at which electric energy is delivered or used in an electric circuit is called electric power. It is converted into another form such as mechanical energy, heat, or light.

30. Electric Power (2)
If a lamp rated at 120 watts operates on a 120-volt line, it will draw a current of 1 ampere (120 watts = 1 ampere × 120 volts).
A 60-watt lamp draws 1/2 ampere on a 120-volt line.
Calculating the cost of electrical energy: A kilowatt is 1000 watts, and a kilowatt-hour represents the amount of energy consumed in 1 hour at the rate of 1 kilowatt. Therefore, in a locality where electric energy costs 5 cents per kilowatt-hour, a 100-watt electric light bulb can be run for 10 hours at a cost of 5 cents, or a half cent for each hour. A toaster or iron, which draws much more current and therefore much more energy, costs about ten times as much to operate.

31. Power Calculations
The power and voltage on the light bulb read “100 W , 120 V.” How many amperes will flow through the bulb?
100 W = current x 120 V
current =100/120 = 5/6 A = .83 A

32. More Calculations
1. If a 120-V line to a socket is limited to 15 A by a safety fuse, will it operate a 1200-W hair dryer? 2. At 10¢/kWh, what does it cost to operate the 1200-W hair dryer for 1 h?
Power = 15 A x 120 V = 1800 Watt (yes!)
1200 Watt = 1.2 KWatt
Cost = 1.2 KW x 1h x 0.1$ = 0.12$

33. ConcepTest 17.1 Connect the Battery
Which is the correct way to light the lightbulb with the battery?
4) all are correct
5) none are correct 1) 2) 3) 33

34. ConcepTest 17.1 Connect the Battery
Which is the correct way to light the lightbulb with the battery?
4) all are correct
5) none are correct 1) 2) 3)
Current can only flow if there is a continuous connection from the negative terminal through the bulb to the positive terminal. This is only the case for Fig. (3). 34

35. Series Circuits
Electric current has but a single pathway through the circuit. This means that the current passing through each electrical device is the same.
This current is resisted by the resistance of the first device, the resistance of the second, and that of the third also, so the total resistance to current in the circuit is the sum of the individual resistances along the circuit path.
The current in the circuit is numerically equal to the voltage supplied by the source divided by the total resistance of the circuit. This is in accord with Ohm's law.
Ohm's law also applies separately to each device. The voltage drop, or potential difference, across each device is proportional to its resistance. This follows from the fact that more energy is used to move a unit of charge through a large resistance than through a small resistance.
The total voltage impressed across a series circuit divides among the individual electrical devices in the circuit so that the sum of the voltage drops across each individual device is equal to the total voltage supplied by the source.

36. Series Circuits 2 Current the same through every load.
Series Connections:
Total Resistance = Sum of individual Resistances.
Current the same through every load.

37. Example Series
Given: Three bulb s with the resistances R1=4Ω, R2=6 Ω, R3=12Ω, are connected in series with a 6 V battery. Required to find:
a) The equivalent resistance of the bulbs Rs
b) The current flowing through each bulb
c) The voltage drop across each bulb:
d) The power dissipated by each bulb:

38. Parallel Circuits
Each device connects the same two points A and B of the circuit. The voltage is therefore the same across each device.
The total current in the circuit divides among the parallel branches. Since the voltage across each branch is the same, the amount of current in each branch is inversely proportional to the resistance of the branch—Ohm's law applies separately to each branch.
The total current in the circuit equals the sum of the currents in its parallel branches.
As the number of parallel branches is increased, the overall resistance of the circuit is decreased. Overall resistance is lowered with each added path between any two points of the circuit. This means the overall resistance of the circuit is less than the resistance of any one of the branches.

39. Parallel Connection Voltage: the same
Different parts of an electric circuit are on separate branches.
Voltage: the same
Total current: sum of currents in each branch.
Resistance:

40. Example Parallel
Given: Three bulb s with the resistances R1=4Ω, R2=6 Ω, R3=12Ω, are connected in parallel with a 6 V battery. Required to find:
a) The equivalent resistance of the bulbs Rp
b) The current flowing through each bulb and the total current:
c) The voltage drop across each bulb:
d) The power dissipated by each bulb:

41. ConcepTest 18.1a Series Resistors I
1) 12 V
2) zero
3) 3 V
4) 4 V
5) you need to know the actual value of R
Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential difference across each resistor?
9 V 41

42. ConcepTest 18.1a Series Resistors I
1) 12 V
2) zero
3) 3 V
4) 4 V
5) you need to know the actual value of R
Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential difference across each resistor?
Since the resistors are all equal, the voltage will drop evenly across the 3 resistors, with 1/3 of 9 V across each one. So we get a 3 V drop across each.
9 V
Follow-up: What would be the potential difference if R= 1 W, 2 W, 3 W ? 42

43. ConcepTest 18.1b Series Resistors II
1) 12 V
2) zero
3) 6 V
4) 8 V
5) 4 V
In the circuit below, what is the voltage across R1?
12 V
R1= 4 W
R2= 2 W 43

44. ConcepTest 18.1b Series Resistors II
1) 12 V
2) zero
3) 6 V
4) 8 V
5) 4 V
In the circuit below, what is the voltage across R1?
The voltage drop across R1 has to be twice as big as the drop across R2. This means that V1 = 8 V and V2 = 4 V. Or else you could find the current I = V/R = (12 V)/(6 W) = 2 A, then use Ohm’s Law to get voltages.
12 V
R1= 4 W
R2= 2 W
Follow-up: What happens if the voltage is doubled? 44

45. ConcepTest 18.2a Parallel Resistors I
2) zero
3) 5 A
4) 2 A
5) 7 A
In the circuit below, what is the current through R1?
10 V
R1= 5 W
R2= 2 W 45

46. ConcepTest 18.2a Parallel Resistors I
2) zero
3) 5 A
4) 2 A
5) 7 A
In the circuit below, what is the current through R1?
10 V
R1= 5 W
R2= 2 W
The voltage is the same (10 V) across each resistor because they are in parallel. Thus, we can use Ohm’s Law, V1 = I1 R1 to find the current I1 = 2 A.
Follow-up: What is the total current through the battery? 46

47. Summary of Terms
 Potential difference (synonymous with voltage difference) The difference in electric potential between two points, measured in volts. When two points having different electric potential are connected by a conductor, charge flows as long as a potential difference exists.  Electric current The flow of electric charge that transports energy from one place to another. Measured in amperes, where 1 A is the flow of 6.25 × 1018 electrons per second, or 1 coulomb per second.  Electrical resistance The property of a material that resists electric current. Measured in ohms (Ω).
 Ohm's law The statement that the current in a circuit varies in direct proportion to the potential difference or voltage across the circuit and inversely with the circuit's resistance. A potential difference of 1 V across a resistance of 1 Ω produces a current of 1 A.  Direct current (dc) Electrically charged particles flowing in one direction only.  Alternating current (ac) Electrically charged particles that repeatedly reverse direction, vibrating about relatively fixed positions. In the United States the vibrational rate is 60 Hz.  Electric power The rate of energy transfer, or the rate of doing work; the amount of energy per unit time, which electrically can be measured by the product of current and voltage. Measured in watts (or kilowatts), where 1A × 1V = 1W.
 Series circuit An electric circuit in which electrical devices are connected in such a way that the same electric current exists in all of them.
 Parallel circuit An electric circuit in which electrical devices are connected in such a way that the same voltage acts across each one and any single one completes the circuit independently of all the others.