Physics 331 Test 2 Review
Wye-Delta Transformations: This transformation is useful when components are not in
series or in parallel
R1
R2
RA

R3
RB
RC
R R  R 2 R 3  R 1R 3
R AR B
RA  1 2
RA  RB  RC
R3
The same pattern holds for the other resistor transformations
R1 
R1 R 2

R3 R4
Voltage and Current Source Conversions: Know how to convert from a real voltage
source to a real current source and vice versa.
Balanced Bridges
Solving Simultaneous Equations: Know Cramer’s Rule and how to write the solution to
simultaneous equations in Matrix form.
Mesh Analysis: (Procedure)
(1) convert all real current sources to real voltage sources
(2) choose direction of current through each section of the circuit
(3) choose the direction of the closed loops in the circuit
(4) use Kirchhoff’s voltage law around two or more closed loops to write equations for
the current
(5) solve the simultaneous equations
Nodal Analysis: (Procedure)
(1) convert all real voltage sources to real current sources
(2) identify all nodes and choose a reference node
(3) label the other nodes with corresponding voltages
(4) make an arbitrary assumption about the magnitudes of the voltages V1 > V2 > . . .
(5) label the current across each resistor and pay close attention to the direction,
remember current flows from a higher to a lower potential
(6) use Kirchhoff’s current law at each node
(7) solve the simultaneous equation for the voltages
Superposition Principle: (Procedure)
(1) remove all sources accept one
(a) replace ideal voltage sources by short circuits
(b) replace ideal current sources by open circuits
(2) compute the current through or voltage across each device when one source is present
(3) repeat this process for each source
(4) add all computed values for each device pay close attention to the direction of the
currents
Thevenin’s Theorem: (Procedure)
(1) open circuit the terminals with respect to the devices which are to be replaced by the
Thevenin equivalent circuit
(2) determine RTH = total resistance at the open circuit terminals when
(a) voltage sources are replaced by short circuits
(b) current sources are replaced by open circuits
(3) determine ETH = the voltage across the open terminals
(4) replace the terminals by ETH and RTH.
Norton’s Theorem: (Procedure)
(1) find the Thevenin Equivalent circuit
(2) replace real voltage source by real current source
or
(1) find the Thevenin Equivalent resistance
(2) short circuit the open terminals and determine the current through the short this will
give the Norton Equivalent current.
Maximum Power Transfer Theorem:
Maximum power is developed in a load when the load resistance equals the Thevenin
resistance of the source to which it is connected.
Millman’s Theorem:
Parallel connected real current sources can be replaced by a single equivalent real current
source and more generally parallel connected real voltage sources can be replaced by a
single equivalent real voltage source.
parallel real voltage sources:
(1) convert real voltage sources to real current source
(2) find single equivalent real current source
(3) convert real current source to real voltage source
Formulas
Ohm’s Law V = I R
Power dissipated in a resistor in the form of heat
P=VI=I2R=V2/R
Resistors in Series RT = R1 + R2 + R3 + . . .
Kirchhoff’s Voltage Law: The sum of the voltage drops around any closed loop
equals the sum of the voltage rises around that loop.
Vrise 
Vdrop (around any closed loop)


Voltage Divider Law:
Vx  V
Rx
RT
1
1
1
1



 ...
R T R1 R 2 R 3
Kirchhoff’s Current Law: The sum of all current entering a junction, or any portion of
a circuit, equals the sum of the current leaving the same.
Resistors in Parallel:
I
enter
  I exit (any junction)
Current Divider Rule:
Ix  I
RT
Rx
Wye-Delta Transformations:
R1
R2
RA

R3
RB
RC
R R  R 2 R 3  R 1R 3
R AR B
RA  1 2
RA  RB  RC
R3
The same pattern holds for the other resistor transformations
R1 
Balanced Bridges
R1 R 2

R3 R4
Maximum Power Transfer Theorem:
PL
MAX

E 2 TH
4 R TH
1.
Find the total current drawn from the voltage source in the circuit shown below by
performing a Y or  transformation.
5 k
4 k
6 k
2 k
15V
3 k
2.
1 k
Use Mesh analysis to determine the current through the 15  resistor shown in the
figure below. Draw arrows on the schematic diagram (or on a redrawn version of
the circuit) showing the direction of the current through each section as required
by Mesh analysis. Also be sure to indicate the direction of the current through the
15  resistor.
5
4A
15 
10 
15 V
5
3.
Write the equations necessary to analyze the circuit shown below by nodal
analysis. Express the equations in matrix form. Write the matrix form of the
solution for each value of V. Do not evaluate the determinants, simply write the
answer in matrix form. Be sure to label the voltages on the schematic diagram and
the direction of the currents.
6A
5
2
8A
2A
4.
3
4
Use the superposition principle to determine the current through the resistor R1.
Indicate the direction of the current on the schematic diagram.
100VV
100
30 

30
20
RR1 1==20
5A
60 
10
10AA
24
24
5.
Find the Norton Equivalent Circuit to the left of the terminals x y. (Millman’s
Theorem may be useful) If the resistor, R, has a value R = 50 k, what is the
power dissipated in that resistor.
x
40V
5mA
50k
3mA
R
100k
20k
y
6.
For the circuit shown below
(a) find the value of RL necessary to obtain maximum power in RL and
(b) find the maximum power in RL.
50 V
20 
40 
RL
80 
60 
2A