Principles of Technology
Chapter 10 Electric Current & Circuits 1
Name______
KEY OBJECTIVES At the conclusion of this chapter you will be able to:
• Define the term electric current, and state the SI unit for it.
• Solve problems involving current, charge, and time.
• Distinguish between conventional current and electron flow.
• Define the term resistance, and state the SI unit for it.
10.1 INTRODUCTION
In Chapter 9, we learned about static charges. In this chapter we learn about charges in motion and the
way they function in electric circuits. Without electric circuits it would be impossible to operate most of
the devices that we take for granted, such as televisions, telephones, blenders, and vacuum cleaners.
10.2 ELECTRIC CURRENT
The word current means “flow” and electric current means “flow of charge.” When we use the term
electric current, we are referring, not to the speed of the charged particles, but to the quantity of charge
that passes a single point in time.
As an analogy, consider the movement of cars on a highway. We measure the speed of a single car by
calculating the distance it travels in a given amount of time. We measure the flow of traffic by counting
the number of cars passing a given point in a given amount of time. During rush hour, the flow of traffic
will be high, but the speed of any individual car may be quite small. At 4 A.M., however, the reverse is
likely to be true.
The SI unit of current is the ampere (A) which is equivalent to 1 coulomb per second. The symbol
used to represent current is I, and we can write:
I = ∆q / t
PROBLEM
What is the electric current (I) in a conductor if 240 coulombs (q) of charge pass through it in 1.0
minute (t)?
SOLUTION
We solve the problem by using the relation I = Δq/t and remembering that time must be in seconds.
I = Δq/t = 240 C / 60 s = 4.0 A
In metallic conductors, the current is carried by freely moving electrons; in solutions, the current is carried
by ions; in gases, the current is carried by both electrons and ions.
Assessment Question 1
When a charge of 85 coulombs (Δq) is moved in a wire in 120 seconds (t), calculate the electric current
(I) in the wire. (I=Δq/t)
a) 0.71 A
b) 1.4 A
c) 35 A
d) 205 A
Assessment Question 2
Calculate the charge (Δq) that is moved in a wire in 3 minutes (t) if an electric current of 18 A (I) moves
through the wire. (I =Δq/t)
(1 minute = 60 seconds)
a) 17 C
b) 60 C
c) 540 C
d) 3240 C
Assessment Question 3
How much time (t) does it take for a charge of 1500 coulombs (Δq) to move through a wire with an
electric current of 25 A (I) in the wire.
(I=Δq/t)
(1 minute = 60 seconds)
a) 0.17 s
b) 1 minute
c) 6 hours
d) 250 seconds
10.3 CURRENT AND POTENTIAL DIFFERENCE
How do we establish a current in a conductor? To initiate the flow of
charge, we find that a potential difference is necessary:
We can see from the diagram that the potential difference is oriented
so that positive charges will flow toward the right (the negative
terminal) while negative charges (including electrons) will flow
toward the left (the positive terminal).
We call the flow of positive charges a conventional current, and its direction is always opposite to the
direction of electron flow. A conventional cur rent is equivalent to an electron flow of the same magnitude
in every respect except direction. In this book, when we speak of the direction of the current, we are
referring to conventional current.
10.4 RESISTANCE
Suppose we removed the source of potential difference in the diagram in Section 14.3. What would
happen to the flow of charge in the conductor? We know what would happen: the current would cease. A
real-life situation of this type is turning off the switch of a lit lamp.
The reason the current ceases is that, as charges travel through the conductor, they lose energy because of
collisions with the atoms of the conductor. This situation is roughly analogous to an object’s coming to
rest on a surface because of friction. We call the electrical analog of friction resistance. An effect of
electrical resistance is the almost total conversion of the lost energy into heat. Resistance is the reason that
wires become hot as they conduct a current.
We measure the resistance of a material by placing a potential difference across it and then measuring the
amount of current that passes through the material. Resistance is defined as the ratio of potential
difference to current:
R=V/I
The SI unit of resistance is the volt per ampere (V/A), which is called the ohm ( in honor of German
physicist Georg Ohm.
PROBLEM
When a conductor has a potential difference of 110 volts (V) placed across it, the current through it is 0.50
ampere (I). What is the resistance (R) of the conductor?
SOLUTION
R = V / I = 110 V / 0.50 A = 220 Ω
Assessment Question 4
When a wire has a potential difference of 342 volts (V) and a current of 15 A (I), calculate the resistance
(R) in the wire.
(R=V/I)
a) 0.04 Ω
b) 1.4 Ω
c) 23 Ω
d) 190 Ω
Assessment Question 5
What is the potential difference (V) in a silicon rod with a current of 13 A (I) and a resistance of 23 Ω (R).
a) 0.57 V
b) 1.8 V
c) 36 V
d) 300 V
(R=V/I)
Assessment Question 6
What is the current (I) in an electric cord with a potential difference of 110 volts (V) and a resistance of
0.0005 Ω (R).
(R=V/I)
a) 55 A
b) 115 A
c) 5200 A
d) 220,000 A
The resistance of a material depends on (1) the nature of the material, (2) the geometry of the conductor,
and (3) the temperature at which the resistance is measured.
1. Metallic substances are good conductors; that is, they have
low resistances. Silver and copper are the best metallic
conductors. The quantity that measures how well a substance resists
carrying a current is known as the resistivity (ρ); its unit is the ohm
meter (Ω∙m).
The table showed lists the resistivities of some common materials.
2. The resistance of a regularly shaped conductor is directly
proportional to its length and inversely proportional to its crosssectional area. This fact makes sense because making a conductor
longer increases the likelihood that the electron will collide with
the atoms of the conductor, thereby increasing the resistance.
Making a conductor wider increases the number of paths that
the electrons can take and, therefore, decreases the resistance.
3. Generally, the resistance of a metallic conductor increases with rising temperature. This fact also
makes sense because increasing the temperature of a conductor increases the vibrational kinetic energy of
its atoms, making collisions with electrons more likely. In other materials, such as semiconductors,
resistance actually decreases with increasing temperature. (We will study the reasons for this phenomenon
in Chapter 14.) In practice, a temperature such as 20°C is chosen as a standard temperature for comparing
resistances.
Assessment Question 7
Which of the following materials has the least resistance to electric current flow?
a) glass
b) iron
c) A short, wide cold silver wire
d) A long, thin hot silver wire
We can combine all of these factors into one relationship (at a specified temperature:
where L represents the length of the conductor and A is its cross-sectional area.
R = ρ∙ L / A
PROBLEM
Calculate the resistance (R) at 20°C of an aluminum wire that is 0.200 meter (L) long and has a crosssectional area of 1.00 x l0-3 square meter (A).
SOLUTION
We know from the table given above that aluminum has a resistivity of 2.65 x 10-8 Ω∙m. Therefore:
R = ρ∙ L / A
R = 2.65 x 10-8 Ω∙m (0.200 m / 1.00 x l0-3 m2)
R = 5.30 x l0-6 Ω
Assessment Question 8
Calculate the resistance (Ω) at 20°C of an iron wire with a resistivity of 9.7 x l0-8 Ω∙m (ρ) that is 1.5
meter long (L) and has a cross-sectional area of 9.7 x l0-3 m2 (A).
(R = ρ∙L/A)
a) 5.0 x l0-3 Ω
b) 1.5 x l0-5 Ω
c) 2.6 x 10-6 Ω
d) 4.0 x l0-7 Ω
Assessment Question 9
Calculate the resistance (Ω) at 20°C of a silicon rod with a resistivity of 60 Ω∙m (ρ) that is 0.5 meter
long (L) and has a cross-sectional area of 0.2 m2 (A).
(R = ρ∙L/A)
a) 0.02 Ω
b) 7.5 Ω
c) 30 Ω
d) 120 Ω
Certain substances, called superconductors, lose all of their resistance when cooled to very low
temperatures. It is also interesting that superconductors do not conduct very well at higher
temperatures. If a substance could be made to be superconducting at or near atmospheric
temperatures, vast quantities of energy could be conserved because the heat lost by superconducting
wires would be minimal.
Assessment Question 10
Which set of statements is true:
i. Superconductors, lose all of their resistance when cooled to very low temperatures
ii. Superconductors conduct better at higher temperatures.
iii. Energy is conserved in superconductors because the heat lost by resistance is minimal..
iv. Metallic substances are good conductors and have less resistance than superconductors at very low
temperatures.
v. Long, thin wires have greater resistance than short, thick wires made of the same metal.
a) i , iv, v
b) i , iii, iv
c) ii , iii, v
d) i , iii, v