Series Circuits
Series Circuit Characteristics
o  Current Characteristics – the current at any point
in a series circuit must equal the current at every
other point in the circuit
Insert Figure 4.5
IT = I1 = I2 = I3…
Voltage Relationships: Kirchhoff’s Voltage Law
o Kirchhoff’s Voltage Law
 The sum of the component
voltages in a series circuit
must equal the source voltage
Series Circuit Characteristics
o  Voltage Characteristics
where
VS
Vn
= the source (or total) voltage
= the voltage across the highest
numbered resistor in the circuit
Kirchhoff’s Voltage Law,
o  Example:
10 V = 8V + 2V
Resistors in Series
A series connection has a single path from
the battery, through each circuit element in
turn, then back to the battery.
Resistors in Series
The current through each resistor is the same;
the voltage depends on the resistance. The
sum of the voltage drops across the resistors
equals the battery voltage.
(since V=IR)
Resistors in Series
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit).
Parallel Circuits
Parallel Circuit Characteristics
o  Parallel Circuit – a circuit that provides more than one
current path between any two points
Parallel Circuit Characteristics
o  Voltage and Current Values
 Voltage across all components, or
branches, is equal.
 Current through each branch is
determined by the source voltage and
the resistance of the branch.
Parallel Circuit Characteristics
o  Current Characteristics
where
In = the current through the
highest-numbered branch in the
circuit
Resistors in Parallel
A parallel connection splits the current; the
voltage across each resistor is the same:
Voltage in a Parallel Circuit
o Since the voltage of each branch is
equal ( V1 = V2 = V3 = Vs )…
Resistors in Parallel
This
gives the reciprocal of the equivalent
resistance:
Increase resistors in parallel means decrease resistance overall!
E
I
R2
R1
As more resistors are
added IN PARALLEL,
more paths are also
added. Total current
increases, so total
resistance must
decrease.
E
R1
I1
R2
I2
R3
I3
Parallel Circuit Characteristics
o  Resistance Characteristics – the total
circuit resistance is always lower than any
of the branch resistance values
Series vs. Parallel Circuits
Series Circuits
o  A series circuit is a circuit in which the current can only
flow through one path.
o  Current is the same at all points in a series circuit
Parallel Circuits
o  In contrast, in a parallel circuit, there are multiple
paths for current flow.
o  Different paths may contain different current flow.
This is also based on Ohm’s Law
Total resistance in a parallel circuit
1=
1 + 1 + 1 + 1_
Rtot R1
R2
R3
Rn
o  Total resistance will be less than the smallest
resistor**
Solving Circuit Problems
Series Circuit Analysis
A 4V battery is placed in a series circuit with a 2Ω resistor.
What is the total current that will flow through the circuit?
V = IR
2Ω
4V = I (2 Ω)
I = 2A
4V
I=?
Series Circuit Analysis
What voltage is required to produce 2 amps through a
circuit with a 3Ω resistor?
V = IR
3Ω
V = 2A ( 3Ω)
V = 6V
?
I = 2amps
Series Circuit Analysis
What resistance is required to limit the current to 4amps if
a 12 V battery is in the circuit?
V = IR
R=?
12 =(4A)R
R = 3Ω
12V
I = 4amps
Series Circuit Analysis
What is the current in the circuit below?
2Ω
12V
4Ω
I=?
Series Circuit Analysis
What is the current in the circuit below?
Recall that resistance in series sum together when
calculating total resistance
V = IR
12 = I (2Ω + 4Ω)
2Ω
4Ω
I = 2A
12V
I=?
Series Circuit Analysis
What is the resistance of the light bulb?
V = IR
12V = 4A (2Ω + R)
R=?
2Ω
R = 1Ω
12V
I = 4A
Voltage
o  What is the voltage drop across each resistor?
2Ω
12V
4Ω
I = 2A
Voltage
o  The voltage drop across each resistor can be
calculated with Ohm’s law
o  The algebraic sum of all voltages in a complete
circuit is equal to the total voltage at the power
source
4V
2Ω
8V
4V
0V
12V
12V
I = 2A
4Ω
12V
Kirchhoff’s Law of Voltages
o  Calculate the total current flow and the voltage drop
across each resistor
o  What will be the voltage drops at points, a, b, c and d
a : 0V
b : 9V
c : 21V
d : 24 V
3V
1Ω
c
12V
4Ω
d
24V
I = 3A
b
9V
a
3Ω
Parallel Circuits
What is the total current below?
1. First calculate total resistance
1 =
1 + 1 + 1
Rtot
5
10
30
1 =
Rtot
1
3
Rtot = (1/3)-1
Rtot = 3 Ω
5Ω
10Ω
30V
30Ω
2. Then use V = IR
30V = I ( 3 Ω)
I = 10A
Parallel Circuits
What is the current through a?
10A
What is the current through e?
10A
What is the current thru each branch b-d?
Same voltage is across each path
b: V = IR 30V = I(5Ω), I= 6A
c: 30V= I(10Ω) , I= 3A
d: 30V= I(30Ω) , I= 1A
e
b
5Ω
c
10Ω
d
30V
Itot = 10A
30Ω
a
Compound Circuits
Total resistance:
o  In compound circuits, reduce all parallel parts to a single
resistance until you have a simpler series circuit
o  The resistance between a and d is 2 Ω
o  Therefore, total resistance is 4 Ω… (2 + 2)
b
3Ω
e
d
a
2Ω
c
20V
6Ω
Compound Circuits
Total current:
V=IR
20V = I (4 Ω)
Itot = 5A
b
3Ω
e
d
a
2Ω
c
20V
6Ω
Compound Circuits
Current flow through b
o  We need to know the voltage drop across b-d
o  Voltage drop across e-d will be 10V (V = 5A  2 Ω)
o  Therefore, voltage drop across each parallel branch (c
and b) must be 10V
o  Current flow in b: 10 = I  3 Ω; = 3.33A
o  Current flow in c: 10 = I  6 Ω; = 1.67A
b
3Ω
e
d
a
2Ω
c
6Ω
20V
Itot= 5A
Compound Circuits
Current flow through b
o  Alternatively, we calculated earlier that the total
resistance of the parallel portion of the circuit was 2 Ω
o  Therefore, the voltage drop across a-d is 10V (V = ItotR)
o  We can now proceed
b
3Ω
e
d
a
2Ω
c
6Ω
20V
Itot= 5A
Compound Circuits
What is the:
o  Total resistance? 4Ω
o  Total current flow? 5A
o  Current flow through b? 3.33A
o  Current flow through c? 1.67A
o  Current flow through d? 5A
o  Voltage between b and d? 10V
o  Voltage between c and d? 10V
o  Voltage between d and e? 10V
e
d
2Ω
b
3Ω
a
c
20V
6Ω
More Practice Simplifying Parallel Circuits
2Ω
1.
5Ω
8Ω
12Ω
9Ω
10Ω
Simplifies to…
2Ω
8Ω
2.
12Ω
24Ω
More Practice Simplifying Parallel Circuits
2Ω
8Ω
2.
24Ω
12Ω
Simplifies to…
Simplifies to…
2Ω
4.
6Ω
3.
12Ω
20Ω
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 Ω)
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
10Ω
V
20Ω
I
30Ω
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)
Current through each resistor would be lower (b/c total current
decreased, but same through each one)
10Ω
V
20Ω
I
30Ω
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” (10Ω)
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)
10Ω
20Ω
V
I
30Ω
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
10Ω
20Ω
V
I
30Ω