Chapter 3
Engr228
Circuit Analysis
Dr Curtis Nelson
Chapter 3 Objectives
•  Be able to recognize resistors connected in series and in
parallel and use the rules for combining them to yield
equivalent resistance;
•  Know how to design simple voltage-divider and currentdivider circuits;
•  Be able to use voltage and current division appropriately to
solve simple circuits;
•  Be able to use ammeters, voltmeters, and ohmmeters correctly.
Series Connections
•  Elements connected head-to-tail and carrying the same current
are said to be connected in series.
Resistors in Series
Voltage Division
Resistors in series “share” the voltage applied to them.
Voltage Divider Example
Calculate V1 using the voltage divider equation.
6K
V1
10V
4K
V1 = 4.00V
Voltage Divider for N Resistors
General form of N resistors connected in series:
Parallel Connections
•  Elements in a circuit connected head-to-head and tail-to-tail
have a common voltage across them and are said to be
connected in parallel.
Resistors in Parallel
Two Resistors in Parallel
Two resistors in parallel can be
combined using the product/sum
shortcut.
Connecting resistors in parallel makes
the equivalent resistance smaller.
Current Division
Resistors in parallel “share” the current through them.
Current Divider Example
Calculate the current in the two resistors below using the
current divider equation.
1mA
i2K = 0.667mA
i4K = 0.333mA
2K
4K
Textbook Problem 3.5d Nilsson 10th
Compute the equivalent resistance seen by the source.
Answer: R = 120Ω
Textbook Problem 3.57 Hayt 7E
Compute the equivalent resistance of the circuit below.
Answer: R = 5.5KΩ (5500Ω)
Measuring Voltage and Current
•  An ammeter is an instrument designed to measure current; it is
placed in series with the circuit element whose current is being
measured.
•  A voltmeter is an instrument designed to measure voltage; it is
placed in parallel with the element whose voltage is being
measured.
Measuring Resistance
•  An ohmmeter is an instrument designed to measure resistance;
it is placed in parallel with the resistive circuit whose
resistance is being measured. Note that accurate measurements
of resistance require that the resistive circuit have no energy
present (no voltage or current).
•  Often, one instrument is used to measure all three parameters,
but not all at once.
Fluke Multi-meters
Measuring Voltage, Current, and Resistance
•  An ideal meter has no effect on the circuit variable being
measured.
•  That means when an ammeter is placed in series to measure
the current through an element, it should have an equivalent
resistance of 0Ω.
•  That means when a voltmeter is placed in parallel to measure
the voltage across an element, it should have an equivalent
resistance of ∞ Ω.
Textbook Problem 3.34 Nilsson 9th
An ammeter with an internal resistance of 0.1Ω is used to
measure i0 in the circuit shown below. Find the percentage
error in the measured value using the following formula:
%Error = [(Measured value – True value)/True value]*100%
Answer: % error = -0.17%
Example: Circuit Simplifying
Find i and the power supplied by the 80V source.
Answer: i = 3 A and p = 270 W supplied
Example
Find V1 in the circuit below:
10V
2K
2K
4K
2K
V1 =
×10V = 3.33V
2K + 4K
+
V1
-
Example
Find I in the circuit below:
+
I
Vx
4Ω
5V
1V
2Ω
+
-
3Vx
− 5 + 4 I + 1 + 2 I + 3Vx = 0, (Vx = 4 I )
− 5 + 4 I + 1 + 2 I + 12 I = 0
18 I = 4
I = 0.222 A
Example
Find the voltage, current, and power associated with each
element in the circuit below:
120A
Answer:
1/30Ω
30A
1/15Ω
v par = 2 V , i1 = 60 A, i2 = 30 A
PR1 = 120W , PR 2 = 60 W
P120 A = −240W , P30 A = 60 W
Chapter 3 Summary
•  Showed how to recognize resistors connected in series and in
parallel, and how to use the rules for combining them to yield
equivalent resistance;
•  Explained how to design simple voltage-divider and currentdivider circuits;
•  Explained the use of voltage and current division;
•  Showed how to use ammeters, voltmeters, and ohmmeters
correctly.