1. Free Electrons & Current
A stable atom has the same number of electrons and protons and is therefore electrically neutral.
However, free electrons can be produced by applying a force to the atom.
The movement of free electrons along a wire is electric current

2. Current, Voltage, Resistance
Current is the rate of flow of electrons/charge
It is abbreviated as I
It is measured in amperes
One ampere is defined as one coulomb (Q; 6.28 X 1018) of electrons flowing past a point each second (Q/s)
Voltage is a force that pushes/drives the electrons/charge
It is also referred to as electromotive force or difference in potential.
It is abbreviated as E or EMF
Voltage is measured in volts (v)
Voltage source will have a polarity (negative and positive side)
Current flows from positive to negative
AC/DC: Alternating current (polarity of source reverses) or Direct current (polarity is constant)
Resistances are the barriers to the flow of charge
It is abbreviated as R
It is measured in ohms()

3. Water Example of Electric Circuit
The reservoir is the battery or other voltage source*
Valve is a switch
The water is the charge (electrons)
Water pressure is is the voltage*
The pipe is the conductor (wire)*
The rate of flow (volume/s) is the current*
Constrictions in the pipe represent resistors

4. Ohms Law
Ohms Law
The current in a circuit is proportional to the voltage and inversely related to the resistance
V = I * R
I = V/R
R = V/I E V I R

5. Circuit Diagrams Battery (short side is negative terminal)
Wire conductor
Resistor
Light bulb (or other load)
Open switch
Closed switch
Ground

6. Series Circuit Analysis
A 4v battery is placed in a series circuit with a 2 resistor.
What is the total current that will flow through the circuit?
V = IR
4v = I * 2 
I = 2a 2 4v
I = ?

7. Series Circuit Analysis
What voltage is required to produce 2a though a circuit with a 3 resistor.
V = IR
V = 2a * 3
V = 6v 3 ?
I = 2a

8. Series Circuit Analysis
What resistance is required to limit the current to 4a if a 12 v battery is in the circuit?
V = IR
12 = 4a * R
R = 3
12v
I = 4a

9. Series Circuit Analysis
Resistance in series sum together when calculating total resistance
What is the current in the circuit below?
V = IR
12 = I * (2 + 4)
I = 2a 2 4
12v
I = ?

10. Series Circuit Analysis
Resistance in series sum together when calculating total resistance
What is the resistance of the light bulb?
V = IR
12 = 4 * (2 + R)
R = 1
R = ? 2
12v
I = 4

11. Kirchhoff’s Law of Voltages
The algebraic sum of all voltages in a complete circuit is equal to zero
If we consider the source voltage to be positive, there will be a negative “voltage drop” across each resistor
The voltage drop across each resistor can be calculated with Ohms law
-4v
-8v
12v 4
I = 2 2 4v
12v 0v
12v

12. Kirchhoff’s Law of Voltages
Calculate the total current flow and the voltage drop across each resistor
Relative to point d, what will be the voltage at points, a, b and c
a vs. d= 24v
b vs. d= 15v
c vs. d= 3v
-3v
-12v 1 c 4 d
24v
I = 3 b
-9v a 3

13. Series vs. Parallel Circuits
Series Circuits
A series circuit is a circuit in which the current can only flow through one path.
Current is the same at all points in a series circuit
Parallel Circuits
In contrast, in a parallel circuit, there are multiple paths for current flow.
Different paths may contain different current flow. This is also based on Ohms Law
Total resistance in a parallel circuit
1 =
Rtot R1 R2 R Rn
Total resistance will be less than the smallest resistor**

14. By Analogy: Series Vs Parallel

15. Parallel Circuits What is the total current below?
1. First calculate total resistance
1 =
Rtot
1 =
Rtot
Rtot = 3 
2. Then use V = IR
30v = I * 3 
I = 10a 5
10
30v
30

16. Parallel Circuits What is the current through a?
What is the current through e?
What is the current each branch b-d?
10a
10a
Same voltage is across each path
b: V= IR 30= I*5 I= 6a
c: 30= I*10 I= 3a
d: 30= I*30 I= 1a b 5 e c
10 d a
30v
30
Itot = 10a

17. Shortcuts to Total R in Parallel
If all N branches have the same resistance, total resistance is equal to the resistance of one branch divided by the number of branches
Total resistance=
Total current=
Current in b=
10 3a b 1
30 e c
30 d a
30v
30

18. Shortcuts to Total R in Parallel
If there are only two branches, the total resistance is equal to the product of the resistances divided by the sum of the resistances
Total resistance=
12 * 4 = 3 
12 + 4
12 4
30v

19. Compound Circuits What is the: Total resistance? Total current flow?
Current flow through b
Current flow through c
Current flow through d
Voltage between b and d
Voltage between c and d
Voltage between d and e b 3 e d a 2 c
20v 6

20. Compound Circuits Total resistance:
In compound circuits, reduce all parallel parts to a single resistance until you have a simpler series circuit
The resistance between a and b is 2 
Therefore, total resistance is 4  (2 + 2) b 3 e d a 2 c
20v 6

21. Compound Circuits Total current: V = I*R 20v = I * 4  Itot = 5a b 32 c
20v 6

22. Compound Circuits Current flow through b
We need to know the voltage drop across b-d
Voltage drop across e-d will be 10v (V= 5a * 2 )
Therefore, voltage drop across each parallel branche (c and b) must be 10v
Current flow in b: 10 = I * 3 ; = 3.33a
Current flow in c: 10 = I * 6 ; = 1.67a b 3 e d a 2 c
20v 6
Itot= 5a

23. Compound Circuits Current flow through b
Alternatively, we calculated earlier that the total resistance of the parallel portion of the circuit was 2 
Therefore, the voltage drop across a-d is 10v (V=ItotR)
We can now proceed b 3 e d a 2 c
20v 6
Itot= 5a

24. More Practice Simplifying Parallel Circuits2 5 1. 8 9
12
10 2
24 8
12 2.

25. More Practice Simplifying Parallel Circuits2 8
24 2.
12 2 6
12 3.
20 4.

26. Some Intuitive Questions (and Answers)
In the following circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it?
The resistor with the largest resistance (30 )
Which resistor has the greatest current flow through it?
Same for all because series circuit
If we re-ordered the resistors, what if any of this would change?
Nothing would change
10
20 V I
30

27. Some Intuitive Questions (and Answers)
If we added a resistor in series with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor?
Total resistance would increase
Total current would decrease
Voltage across each resistor would decrease (All voltage drops must still sum to total in series circuit; Kirchhoff’s law of voltages)
Current through each resistor would be lower (b/c total current decreased, but same through each one)
10
20 V I
30

28. Some Intuitive Questions (and Answers)
In the following circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it?
All the same in parallel branches
Which resistor has the greatest current flow through it?
The “path of least resistance” (10)
What else can you tell me about the current through each branch
They will sum to the total I (currents sum in parallel circuits; Kirchhoff’s law of current)
10
20 V
30 I

29. Some Intuitive Questions (and Answers)
If we added a resistor in parallel with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor?
Total resistance would decrease
Total current would increase
Voltage across each resistor would still be V
Current through each resistor would be higher and would sum to new total I
10
20 V
30 I

30. DC Current vs. AC Current
Direct current (DC) flows in one direction the circuit.
Alternating current (AC) flows first in one direction then in the opposite direction.
Same definitions apply to alternating voltage (AC voltage):
DC voltage has a fixed polarity.
AC voltage switches polarity back and forth.
Much of this info was borrowed from: