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Electric Currents
The Electric Battery
See howstuffworks. Another example of conservation of
energy.
Electric Current
Connecting wires (and/or lamps, etc.) to a battery permits
electric charge to flow. The current that passes any point in the
wire in a time t is defined by
OSE:
I = Q/t,
where Q is the amount of charge passing the point. One
ampere of current is one coulomb per second.
We use this symbol for a battery (the short line is negative):
+-
Here’s a really simple circuit.
Don’t try it at home! (Why not?)
Because electric charge is conserved, the
current at any point in a circuit is the same
as the current at any other point in the
same circuit at that instant in time.
+-
current
The current is in the direction of flow of positive charge.
Opposite to the flow of electrons, which are usually the charge
carriers.
+-
current electrons
An electron flowing from – to + gives rise to the same
“conventional current” as a proton flowing from + to -.
“Conventional” means our convention is always to consider the
effect of + charges.
Example: A steady current of 2.5 A flows in a wire for 4.0 min.
(a) How much charged passed through any point in the circuit?
Q
I 
t
Q  I t
ΔQ =  2.5  4.0  60 
Minutes are
not SI units!
ΔQ = 600 C
(b) How electrons would this be?
total charge
number of electrons =
charge of an electron
600 C
21
number of electrons =
=
3.8×10
electrons
-19
 1.6×10 C 


electron


“This is a piece of cake so far!”
Don’t worry, it gets “better” later.
Ohm’s Law
It is experimentally observed that the current flowing through a
wire depends on the potential difference (voltage) causing the
flow, and the resistance of the wire to the flow of electricity.
The observed relationship can be written
OSE:
V = I R,
and this is often called Ohm’s law.
Ohm’s law is not “fundamental.” It is not really a “law” in the
sense of Newton’s Laws. It only works for conductors, and
some things that conduct electricity do not obey Ohm’s law.
The unit of resistance is the ohm, and is equal to 1 Volt / 1
Ampere.
Example
A small flashlight bulb draws 300 mA from its
1.5 V battery.
(a) What is the resistance of the bulb?
V=IR
R=V/I
R = 1.5 / 300x10-3
R = 5.0 
(b) If the voltage dropped to 1.2 V, how would the current
change?
V=IR
I=V/R
I = 1.2 / 5.0
I = 0.24 A
(“If it’s this easy now, does that mean I’ll pay later?”)
Every circuit component has resistance. This is the symbol we
use for a “resistor:”
All wires have resistance. Obviously, for efficiently carrying a
current, we want a wire having a low resistance. In idealized
problems, we will consider wire resistance to be zero.
Lamps, batteries, and other devices in circuits have resistance.
Resistors are often intentionally used in
circuits. The picture shows a strip of five
resistors (you tear off the paper and
solder the resistors into circuits).
The little bands of color on the resistors have meaning. Here
are a couple of handy web links:
http://www.dannyg.com/examples/res2/resistor.htm
http://xtronics.com/kits/rcode.htm
Electric Power
Last week we defined power as the work done by a force
divided by the time it took to do the work.
PF = WF / t
We put a “bar” above the PF to indicate it is really an average
power. We had probably better do that again, hadn’t we.
OSE:
PF =
WF
.
t
We’d better use the same definition this semester! So we will.
Lec25full.ppt derives the OSE for power in a dc circuit.
OSE: P = IV = I2R = V2/R.
Example
An electric heater draws 18.0 A on a 120 V line. How much
power does it use and how much does it cost per 30 day month
if it operates 3.0 h per day and the electric company charges
10.5 cents per kWh. For simplicity assume the current flows
steadily in one direction.
What the heck is a kWh?
What’s the meaning of this assumption
about the current?
We’ll get to the second question in a minute. The current in
your household wiring doesn’t flow in one direction, but
because we haven’t talked about current other than a steady
flow of charge, we’ll make the assumption (which doesn’t wreck
the calculation.)
Remember your steps to solving problems? The first step is to
think. Maybe the step should really be titled “figure out what
kind of problem it is.”
The problem asks for power. Maybe that identifies the problem
type! Next maybe we had better go to our OSE and see
what it says about power.
P = IV = I2R = V2 /R .
This set of three equations is specific to current flowing in a
circuit.
We’re given current and voltage. It should be clear how to
calculate power.
P =IV
P = (15.0 A) (120 V)
P = 1800 W = 1.8 kW
How much does it cost. We are given cost per kWh and we
calculated k above. What is this kWh (and why the odd
capitalization?
(1 kW) (1 h) = (1000 W) (3600 s)
= (1000 J/s) (3600 s)
= 3.6 x 106 J
So a kWh is a “funny” unit of energy. K (kilo) and h (hours) are
lowercase, and W (James Watt) is uppercase.
To get the cost, find the total energy and multiply by the cost
per energy “unit.”
Cost = (1.8 kW) (30 days) (used 3 h/day) ($0.105/kWh)
Cost = (1.8 kW) (30 days) (used 3 h/day) ($0.105/kWh)
Cost = $17
I wonder how much energy we actually used?
Pavg = WF /t
Energy Transformed = WF = Pavg t
Pavg and the P with the bar above it both mean average power.
Energy Transformed = (1800 J/s) (30 d) (3 h used/d) (3600 s/h)
Pavg
time t
Energy Transformed = 583,200,000 Joules used
That’s a ton of joules! Good bargain for $17. That’s about
34,000,000 joules per dollar.
OK, “used” is not an SI unit, but I stuck it in there to help me
understand. And joules don’t come by the ton.
One last quibble. You know from energy conservation that you
don’t “use up” energy. You just transform it from one form to
another.
Power in Household Circuits
I’ll do a little demo on short circuits and electrical safety…
If you want to do that at home, use the really fine steel wool. The coarse
stuff doesn’t work as well. And remember—adult supervision!
Never replace a properly-rated fuse with a higher rated one
(“higher rated” means handles more current.
Alternating Current
This topic is surprisingly complex. We will not explore it here.
We have implicitly been discussing circuits using batteries as a
power source. The current is called direct current (DC),
because it flows in one direction and does not vary with time.
Microscopic View of Electric Current
Here’s the “classical” picture* of the mechanism for the
resistance of a metal:
electron “drift” velocity
E
-
+
+
+
+
+
+
+
+
+
+
+
The voltage accelerates the electron, but only until the
electron collides with a + ion. Then the electron’s velocity is
randomized and the acceleration process begins again.
*There are two things terribly wrong with this “picture.” You can tell me
one right away. So…
Predictions made by this theory are typically off by a factor or
10 or so, but it was the best we could do before quantum
mechanics.
The free electrons move with velocities on the order of 105 or
106 m/s (fast!) but the directions are random. The “drift
velocity” represents the average velocity, or the net “drift” of
the electrons. It is on the order of 0.05 mm/s.
So how come when I flip a light switch, the light comes on “right
away?”