Definitions, circuit types,
and calculations
Developed by John H. Pinkerton,
Texas A&M Physics & Computer Science grad,
High School Math & Science Teacher
Circuits are pathways for the flow of electrons. Electrons
(negative) try to get away from each other, and flow towards
unpaired protons (positive) due to the ELECTRICAL FORCE.
… Protons don’t move because they are 2000 times
bigger than an electron, and they are stuck in the
nucleus…
If electrons
can make it all the way around the circuit, through
every desired part: the circuit is said to be CLOSED. If
there is a break in the wire, a part is burned out, or anything
else prevents the flow of electrons around the circuit, the
circuit is said to be OPEN.
If for any reason electrons are diverted from the path they are
supposed to follow, it is called a SHORT CIRCUIT
The charge on an electron is measured in COULOMBS (C).
One electron has a charge of 1.6 x 10-19 C . Because
electrons are so small and their charge is so tiny, it takes 1.6
million trillion (1.6 quintillion) of them to make 1 Coulomb!
Current is the amount of charge that goes through a given
location per unit of time. In order to have a positive current,
we say it flows in the opposite direction that the electrons go.
1 Coulomb per second (1C/s) is given the name 1 Ampere
(Amp for short), and is the common Physics unit for current
flow.
Most cell phone charges produce a current of 1-3 Amps…
Electrons do not flow without some form of electrical pressure.
This “pressure” is called VOLTAGE, and is measured in Volts
(V)
Voltage may be supplied by the power company (who use
generators or solar panels to produce it), or from some sort of
battery. Sometimes the voltage source is called the ElectroMotive Force, or EMF for short.
Because Voltage really only makes sense when we are
comparing the “electrical pressure” between TWO different
points in a circuit, sometimes we call Voltage the “Potential
Difference”
Sending a steady, one-way flow of electrons through a wire or
circuit is called DC current (Direct Current). Edison wanted to
use DC current to power houses. We still use DC power in
computer circuits…
Tesla proposed that we just alternate between pushing and
pulling on the electrons that are already in the wire or circuit.
In this way, the circuit would continuously have electrons
moving through it without sending any new ones. Today,
houses are provided with this “Alternating Current” (AC) from
the power company.
Your outlets in your house are wired for 110V, and cycle the
current back and forth 60 times per second (60Hz AC).
A resistor can be any circuit part that slows down the flow of
electricity (i.e. any circuit part ). For example, a light bulb is
just an example of a resistor that glows when it gets hot.
Resistance is measured in Ohms (). There are actually parts
manufactured whose only job is to resist the flow of electricity.
These resistors (formal) are usually either peanut shaped
or box shaped.
Resistance goes up in a wire (or circuit part) if it is
1. Narrower
2. Longer, or
3. Hotter.
If we want to show a picture of a circuit, rather than just talking
about it, we don’t actually draw the parts. Instead, we use
symbols to represent each part, and the overall drawing is
called a schematic.
A sample schematic:
If the current has to flow through a resistor (or other part) in order to get
to the rest of the circuit, it is said to be in series.
Here are three resistors in series with each other:
If the current has a choice of where to flow in a circuit, the parts on
those alternate routes are said to be in parallel.
Here are two resistors in parallel with each other:
Rules for Series & Parallel Subcircuits
V = IR
1. The current is the same everywhere
2. The voltage drops across each resistor
… all voltages add to the total
3. Resistors add directly (3 + 2 = 5)
1. The voltage is the same everywhere
2. The current splits at each juncture, but
… all currents add to the total
3. Resistors add inversely (flip – add – flip )
Using Ohm’s Law
& the Power Formula
Any time you have any TWO of either the Voltage, Current
or Resistance you can use Ohm’s Law to solve for the third value:
V = IR
Where V is the voltage, I is the current and R is the resistance…
V
I
R
If you need to calculate the POWER used in
a
P
resistor, use P = IV or P = I2R
This can be done for the whole circuit or
just one resistor…
I
V
Example of A Series Circuit:
R1
R2
Battery
R1
R2
R3
V
I
36V
8V
12V
16V
2A
18
2A
4
6
8
2A
2A
R
Solving:
R
1. We have both I and R for R1. Using V = IR, V1 = 2A x 4 = 8V
3
2. In a series circuit, the current is the same everywhere, so…
I1 = I2 = I3 = Ibattery = 2A
3. Using V = IR for R2 and R3:
V2 = 2A x 6 = 12V
V3 = 2A x 8 = 16V
4. In a series circuit, the resistors ADD, so the circuit resistance
is:
5. In aRseries
circuit,
voltage adds to the total, so:
4 each
+ 6 resistor’s
+ 8 = 18
circuit =
Vbattery =
8V + 12V + 16V = 36V
Example of A Parallel Circuit:
Battery
R1
R2
R3
V
I
R
16V
16V
16V
16V
7A
2.29
2A
1A
8
16
4
4A
Solving:
1. If you ever have any TWO of V,I, or R, use V = IR to solve for the 3rd…
for R1, V = IR = 2A * 8 = 16V
2. Voltage is the same everywhere on a parallel circuit (or subcircuit)…
so, Vtotal, V2 and V3 are also 16V
3. Now, for R2 and R3, we can use V=IR…
R2 = V / I2 = 16V/1A = 16 I3 = V / R3 = 16V/4 = 4A
4. The sum of the currents through all the legs equals the battery current:
Ibattery = I1 + I2 + I3 = 2A + 1A + 4A = 7A
5. To get the equivalent resistance of the circuit (also called the ):
Requivalent = V / Ibattery = 16V/7A = 2.29
Example of HOW to find the
Equivalent Resistance of a Parallel Circuit:
If R1 = 3, R2 = 4 and R3 = 5
Flip-Add-Flip…
First, Flip and add them…
𝟏
𝟑
𝟏
𝟒
+ +
𝟏
𝟓
𝟐𝟎 𝟏
𝟐𝟎 𝟑
= ( )
𝟏𝟓 𝟏
𝟏𝟓 𝟒
𝟏𝟐 𝟏
𝟏𝟐 𝟓
+ ( )
+ ( )
=
𝟐𝟎
𝟔𝟎
+
𝟏𝟓
𝟔𝟎
+
𝟏𝟐
𝟔𝟎
=
𝟒𝟕
𝟔𝟎
Finish by Flipping your answer back…
𝟒𝟕
𝟔𝟎

𝟔𝟎
𝟒𝟕
  1.27 
NOTE: To do this on the calculator, press
1/3+1/4+1/5 <Enter>
1/<Ans> <Enter>
HOW to work a “Combo” Circuit…
1. Remember as you go around the circuit, every time you go across
a series resistor OR set of parallel resistors, the voltage drops…
2. You can turn it into a “Series ONLY” circuit by using Flip-Add-Flip to
compress parallel resistors into a SINGLE equivalent resistor.
3. Once you have done HOWTO #2 above, just work the circuit like a
normal series circuit. When you have the Voltage, Current and
Resistance for each resistor, re-expand back into the original
circuit. Values you’ve figured out still apply 
i.e. – if you figured 2A of current is flowing through
a resistor, when you expand it back into multiples
again, the total current through those will still be 2A
Developed by John H. Pinkerton,
Texas A&M Physics & Computer Science grad,
High School Math & Science Teacher