Resistive Circuit Example Solutions
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Microsim's Design Center (PSpice for Windows) Evaluation version 6.0
or WordPerfect Draw were used to create schematics. Microsoft's
Paintbrush and Leonardo Haddad Loureiro's Lview were used to edit and
convert schematics to .gif format files.
Hints and step-by-step guidance are available in this document. The
problems are from or similar to problems from the sources listed below
which also have many additional practice problems.
- CircuitTutor by Burks Oakley II (highly recommended)
- Electric Circuits by James Nilsson
- Introduction to PSpice by James Nilsson & Susan Riedel
#1. Following the passive sign convention, assign each resistor
(element) voltage with polarity and each resistor (element) element
current with direction. Compute and list the numerical value of each of
these voltages and currents. Also compute the numerical value of Vo as
defined in the schematic.
Following the passive sign convention, assign each resistor
(element) voltage with polarity and each resistor (element) element
current with direction. 
It is suggested that you
label V- the node voltage at inverting input
note that there is a negative feedback path and therefore the input
terminal voltage difference V+- = 0
note that current into op amp input terminals is zero
Compute and list the numerical value of each of these voltages and
currents. 
- Since i+ = 0, i4 = i6 = ( 1 V / (4 k ohms + 6 k ohms)) = 0.1
mA
- V4 = (4 k ohms)(0.1 mA) = 0.4 V
- V6 = (6 k ohms)(0.1 mA) = 0.6 V
- Since V+- = 0, V- = V6 = 0.6 V
- By KVL, V5 = ( 0 - V- ) = ( 0 - 0.6 V) = - 0.6 V
- i5 = ( - 0.6 V / 5 k ohms ) = - 0.12 mA
- Since i- = 0, i50 = i5 = - 0.12 mA
- V50 = (50 k ohms)(- 0.12 mA) = - 6 V
- By KVL, Vo = ( V- - V50) = ( + 0.6 V - ( -6 V)) = + 6.6 V
Determine the value of load resistor that would receive the
maximum electrical power and determine the value of that maximum power.
The plan is to determine the Thevenin equivalent circuit seen by the
load and then set the load resistance equal to the Thevenin Resistance.
One way to determine the Thevenin equivalent circuit seen by the
load is to do a source transformation so that there will be combinable
resistors. 
Combining the parallel resistors, yields 8.57 ohms.
Another source transformation can be done to obtain Thevenin
equivalent seen by load.
Since the resulting voltage divider consists of two equal value
resistors, half of the Thevenin voltage appears across the load. The
electrical power (load current times load voltage) into the load is
((22.9 V / 2)/8.57 ohms)(22.9 V / 2) = 15.2 W.
Write an equation that expresses the node voltage V2 in terms of
the independent source parameters. 
CircuitTutor does this problem as a superposition example.
Since only one supermesh KVL is required, that is a possibility.
Since there is only one KCL required with node analysis that is a
good method.
Result is V2 = (((90 ohm)Ix + Vx)/2)
Determine the numerical value of V1 as defined in the schematic.
Node analysis requires only one KCL. Assign element voltages and
currents according to the passive sign convention.
- Write a Kirchhoff's Current Law (KCL) equation at the top
(essential) node.
- Substitute element equations, for example, id = (0.5)(V1)
- Express everything in terms of the one essential node voltage V.
- Solve for V.
The top-most node is 6 V less positive than the bottom-most node.
The voltage divider formula may be used to infer the numerical
value V1 = - 2V.
Determine the equivalent resistance for each connection shown.
In the first circuit, the 18 k, 22 k and 27 k are in parallel and
may be combined into a 7.24 k ohm resistor. The 15 k is in series with
this combined parallel resistance. The complete equivalent resistance
is(15 k + 7.24 k) = 22.2 k ohms.
In the second circuit, the same curent passes through all resistors
so these series resistances may be added to yield 82 k ohms.
You may want to practice using the Novanet equivalent resistance
drill (circanal)
Assume the voltmeter is ideal and has no current flowing through
it, determine Vo. Determine the value of Vo if the voltmeter has an
equivalent resistance of 10 MW. Write a sentence describing how you
could infer the true no-load voltage from the voltmeter indication
knowing the voltmeter equivalent resistance.
Assume the voltmeter is ideal and has no current flowing through
it, determine Vo. It is suggested that you redraw circuit with just the
independent source and the 1.5 M ohm and 2.2 M ohm resistors. Voltage
divider analysis yields Vo = 59.5 V.
Determine the value of Vo if the voltmeter has an equivalent
resistance of 10 M ohm. A 1.8 M ohm resistance results from the
parallel combination of 10 M ohm and 2.2 M ohm. Voltage divider
analysis yields Vo = 54.6 V.
Write a sentence describing how you could infer the true no-load
voltage from the voltmeter indication knowing the voltmeter equivalent
resistance. From the indication and equivalent resistance, you can infer
the curent in the meter. This is the current flowing through R1 but not
through R2. One more piece of information is needed to infer the true
no-load voltage from the voltmeter indication knowing the voltmeter
equivalent resistance.
Draw the schematic diagram for Thevenin equivalent with respect to
terminals a and b. Your sketch should include numerical values with
polarity indicated. Label terminals a and b in your schematic.
In the interest of time, it is suggested that you use PSpice.
Since the open circuit voltage is the voltage at node a with
respect to node b, node b is chosen as ground or node zero for PSpice.
The output node voltage at node a will be the Thevenin open circuit
voltage. To sense current that controls the dependent source, a dummy
(zero-voltage) independent DC voltage source is inserted in the circuit
.
**** CIRCUIT DESCRIPTION
V1 1 0 0.1
R1 1 2 4K
R2 2 0 21K
VDUM 2 3 0
R3 3 4 1.5K
R4 4 0 600
R5 4 5 20K
R6 5 0 700
F1 5 4 VDUM 40
.TF V(5) V1
.END
The Thevenin open circuit voltage is listed as the node voltage at
the node previously specified as output.
The Thevenin equivalent resistance is listed as the output
resistance at the node previously specified as output.
The Thevenin equivalent circuit is 
Determine the numerical values of Vx, Vy and Vz as defined in the
schematic.
Consistent with the passive sign convention, assign element
currents and draw conventional current direction arrows.
Since two rightmost resistors have same voltage (parallel), they
can be combined into a single resistor. Redraw the circuit maintaining
the identity of Vx, Vy and Vz. 
- Vx = (1000 ohms)(- 6 mA) = - 6 V
- Vy = Vz = (667 ohms)(- 6 mA) = - 4 V
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