Electric Circuits
The transfer of electrical energy takes place via an
electric circuit. This electrical energy is created in some
type of “power plant” that maintains a constant charge.
This charge is then free to move along conducting wires.
One such “power plant” is a battery. A battery uses a
chemical reaction to transfer electrons from one terminal to
another. Because of the difference in charge between the
two terminals, an electric potential is set up
The maximum potential difference that is set up is
called the electromotive force (EMF) of the battery.
For a typical car battery for example, a constant
potential difference of 12 Volts is maintained between the
terminals. A typical flashlight has a potential difference of
1.5 V.
In analyzing an electric circuit, we will use the
following symbol to represent a battery:
Electric Current
When conducting wires are connected to the terminals
of a battery, the charges are free to move.
The quantity that describes how many charges pass a
point in a certain time is called the current.
Thus, the current is defined as:
I = q/t
Question: What is the SI unit of current?
Answer: C/s is given the name Ampere after a French
Mathematician.
If charges are moving in the same direction at all
times, the current is called direct current (dc), which is the
type produced in batteries.
If the charges are constantly changing direction, the
current is called alternating current (ac).
Circuits and Ohm’s Law
We all know that it is the electrons that flow between
the terminals of a battery. Also, we know that they flow
from a region of lower electric potential to a region of
higher electric potential.
However, from what has been conventional for the last
100 years, we will show current flowing in the opposite
direction as in the following figure:
Ohm’s Law
The current that is produced in a battery that “pushes”
its way through the circuit is analogous to water being
pushed through a pipe. The higher the water pressure, the
larger the flow. Thus, the higher the voltage, the larger the
current.
In other words, the voltage is directly proportional to
the current. The higher the voltage, the larger the current.
Also, the way water flows through a pipe is dependent
also on the shape and diameter of a pipe. Longer and
shorter pipes offer more “resistance” to the flow of water.
Similarly, the constant of proportionality will be the
resistance of the wire.
V=IR
Ohm’s Law and Resistors
The first one to discover this was Georg Ohm so it is
called Ohm’s Law.
The SI unit of resistance is called the Ohm and has
units of V/A. We use the Greek letter  to denote
resistance.
Resistors are important in electric circuits because
they limit the amount of current and establish certain
voltage levels.
When we represent resistors in a circuit we use the
following symbol:
Likewise, we will always represent conducting wires
as straight lines.
Like capacitance, we can find the resistance of a
material depending on the geometry and composition of the
resistor. Just like capacitors, capacitors made of different
materials will have different resistances.
Resistance and Resistivity
The resistance of a piece of material of length L and
cross-sectional area A is:
R =  L/A
The quantity  is called the resistivity of the material.
The resistivity is an inherent property of the material.
Insulators such as rubber and wood have large resitivities
whereas aluminum, copper and gold have very low
resistivities.
Lecture Question:
Create an experiment that can test the resistivities of
certain materials.
Electric Power is often mistaken as electric potential.
You will often see “9V of Power!”
However, the power that in contained in a circuit
where there is a current I as a result of the voltage V is:
P=IV
Alternating Current
Many more electrical devices use alternating current
than direct current. Everything that you plug into your
electrical sockets uses alternating current.
Since these sockets produce alternating current, we
will use them in many examples. The source of the
alternating current will be some power generator like a
nuclear power plant.
In electric circuits, we will represent the alternating
current with the following symbol:
The following graph shows the voltage produced
between terminals of an ac generator.
Q. What is its shape?
AC Voltage and Power
This sine function has the following form in time:
V = Vo sin 2  f t
Where Vo is the maximum or peak voltage
f is the frequency in Hz
Because the voltage oscillates, so will the current.
Recall: V = I*R
Therefore:
I = (Vo /R) sin 2  f t
or
I = Io sin 2  f t
Likewise: the power recall is: P = I*V so:
P = Io Vo sin2 2  f t
Final comments on alternating current
The power function is plotted below:
As you can see, the power is not constant but also
oscillates. Thus, we consider the average power which is
½ the peak power or:
A slight rearrangement shows that:
Where IRMS and VRMS are called the root mean square
(rms) current and voltage.
The maximum voltage coming out of your socket is
V=170 V. However, the RMS voltage is 170/2 = 120V!
So, unless otherwise stated, power will be the average
power.