Chapter 19
Electric Currents
Sources of Electromotive Force



Devices supply electrical energy, e.g.
batteries, electric generators
Two (or more) terminals with a
potential difference.
When charge flows out from one
terminal, equal charge flows into the
other terminal
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 the wire
The SI unit of current is Ampere
(A)
Q
• 1 A = 1 C/s
I
t
Example
In a tv tube, 5 x 1014 electrons shoot
out in 4 s. What is the electric
current?
Current: amount of charge flowing
through a point per unit time
Current flows from higher potential to lower potential
I
Ohm’s law
e
e
e=RI
R
I
e
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
V
R
I
Resistance, cont

Units of resistance are ohms (Ω)
•1 Ω = 1 V / A

Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Ohm’s 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
Ohm’s Law
•V=IR

Ohm’s Law is an empirical relationship
that is valid only for certain materials
• Materials that obey Ohm’s Law are said to be
ohmic
Example
A 1.57 V battery connects to a light
bulb. If the current through the bulb
is 0.21 A, what is the resistance of
the bulb?
V=RI
Resistance, R = V/I
[R] = V/A = W (Ohm)
For a fixed potential difference across a resistor,
the larger R, the smaller current passing through it.
Req
Parallel connection
Series connection
R1
R2
R1
R2
R3
R3
Req = R1 + R2 + R3
1/Req =
1/R1+1/R2+1/R3
• Electrical wires can be bent and/or stretched.
• A Node point (branching point) can be moved arbitrarily
along the wire.
There are n identical resistors connected in parallel.
Req?
1/Req = 1/R + 1/R + 1/R + … + 1/R
= n/R
Req = R/n
Ra
(1) 1/Req = 1/Ra + 1/Rb
(2) Req is smaller than Ra and Rb
Rb
20
25
Req ≈ 10
1000 = 1k
2
Req < 2
Practically all the current flows
Though the bottom one!!
Ohm’s law:
e = R·I
I = e/R
= (6 V)/(6 Ohm)
= 1.0 A
R=6
6V
What is the electric potential at ?
We cannot tell the absolute potential at this point.
If e at
is +6 V, then 0 V at
If e at
is +3 V, then -3 V at
For both, the potential diff. is 6 V.
To be able to specify absolute potential at a given point,
we need to specify a reference point “0” potential.
GROUND
R1 = 6
6V
Then, e at
is +6 V.
e = “0”
Electrical Energy and Power

In a circuit, as a charge moves through
the battery, the electrical potential energy
of the system is increased by QV
• 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
Electrical Energy and Power,
cont

The rate at which the energy is lost
is the power
Q
P  V  IV
t

From Ohm’s Law, alternate forms of
power are
2
V
PI R
R
2
Electrical Energy and Power,
final

The SI unit of power is Watt (W)
• I must be in Amperes, R in ohms and V
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
Example



Light bulb 60 W, 120 V. Find
resistance of the light bulb.
Bulbs in series
Bulbs in parallel
Resistivity

The resistance of an ohmic conductor
is proportional to its length, L, and
inversely proportional to its crosssectional area, A
L
R
A
• ρ is the constant of proportionality and
is called the resistivity of the material
A
L
R =  L /A
Resistivity: material parameter
same for any shape in a given material.
[] = W.m
e.g. for copper
 =
gold
 =
tungsten  =
iron
 =
nickel-chrome
1.7 x 10-8
2.44 x 10-8
5.6 x 10-8
9.5 x 10-8
 = 150 x 10-8
Example
A silver wire has a resistance of 2W.
What would be the resistance of a
silver wire twice its length and half
its diameter?
Temperature Variation of
Resistivity

For most metals, resistivity increases
with increasing temperature
• With a higher temperature, the metal’s
constituent atoms vibrate with
increasing amplitude
• The electrons find it more difficult to
pass the atoms
Temperature Variation of
Resistance, cont

For most metals, resistivity increases
approximately linearly with
temperature over a limited
temperature range, resulting
R  Ro [1 (T  To )]



T-To is temperature change
 is the temperature coefficient of resistivity
Ro is the resistance at To
Ag: 3.8 x 10-3 /C
Cu: 3.9 x 10-3 /C
Fe:5.0 x 10-3 /C
Example
Light bulb (60 W; 120 V; 240 W)
operates at 1800 C. What is the
resistance of the filament (tungsten)
at 20 C?