Download REVIEW FOR ELEC 105 MIDTERM EXAM #1 (FALL 2001)

ELEC 225
Circuit Theory I
Fall 2007
Review Topics for Exam #1
The following is a list of topics that could appear in one form or another on the exam. Not all of
these topics will be covered, and it is possible that an exam problem could cover a detail not
specifically listed here. However, this list has been made as comprehensive as possible.
Passive sign convention for Ohm’s law and power calculations
- v = iR or v = −iR
- p = iv or p = −iv
- sign depends on direction of current relative to polarity of voltage
- if p is positive, then power is absorbed (dissipated)
- if p is negative, then power is delivered (supplied)
Power calculations for resistors
v2
- p  i 2 R or p 
R
- power is always dissipated in resistors (p is always positive)
Ideal independent voltage sources
- maintains indicated voltage between its two terminals at all times
- current through source depends on external circuit only
- source has no single value of resistance (i.e., Ohm’s law is not applicable)
- a short circuit can be represented by a voltage source of 0 V
Ideal independent current sources
- maintains indicated current through its branch at all times
- voltage across source depends on external circuit only
- source has no single value of resistance (i.e., Ohm’s law is not applicable)
- an open circuit can be represented by a current source of 0 A
Possible contradictions involving ideal voltage and current sources
- two or more voltage sources of different values in parallel is meaningless
- two or more current sources of different values in series is meaningless
Dependent sources
- voltage-controlled voltage source (current thru source determined by external ckt)
- current-controlled voltage source (current thru source determined by external ckt)
- voltage-controlled current source (voltage across source determined by external ckt)
- current-controlled current source (voltage across source determined by external ckt)
Kirchhoff’s voltage law (KVL)
- simply a restatement of the law of conservation of energy in ckt terms
- voltages around any closed path must add to zero
- sum of voltages around loop = 0
- sum of voltage rises = sum of voltage drops
- voltage rises or drops can be given either positive or negative signs in KVL equation,
but must be consistent within a single KVL equation
- corollary: voltage between two points = sum of voltage drops and rises between
those two points
1
Kirchhoff’s current law (KCL)
- simply a restatement of the law of conservation of mass (charge) in ckt terms
- current flowing into/out of any region of circuit must add to zero
- sum of currents entering = sum of currents leaving
- currents entering or leaving can be given either positive or negative signs in KCL
equation, but must be consistent within a single KCL equation
Series resistors
- all have the same current flowing through them, but different voltages across them
- Req  R1  R2    RN
- if one resistor is order(s) of magnitude larger than the rest, then Req ≈ that value
Parallel resistors
- all have the same voltage across them, but different currents through them
1
- Req 
1
1
1


R1 R2
RN
RR
- special case for only two resistors: Req  1 2
R1  R2
- if one resistor is order(s) of magnitude smaller than the rest, then Req ≈ that value
- equiv. resistance of any finite resistor in parallel with an infinite resistance is equal to
the finite value
Conductance
- G = 1/R
- Ohm’s law for conductances: i = Gv, v = i/G
1
- series conductances: Geq 
1
1
1


G1 G2
GN
- parallel conductances: Geq  G1  G2    G N
Voltage divider
- formed by two or more resistors in series (all must share the same current)
- let total voltage across entire set of resistors = vtot
- let voltage across kth resistor = vk
Rk
- vk 
vtot
R1  R2    RN
Current divider
- formed by two or more resistors in parallel (all must share the same voltage)
- let total current flowing into network of resistors = itot
- let current flowing through kth resistor = ik
Req
itot
- ik 
Rk
R2
R1
- special case for only two resistors: i1 
itot and i2 
itot
R1  R2
R1  R2
Gk
- using conductances: ik 
itot
G1  G2    GN
2
Nodal analysis
- based on KCL applied to all nodes except reference node
- definition of node voltage: voltage measured between a node and the reference node
(ground); pos. side at node, neg. side at ground
- express currents flowing through resistors in terms of node voltages (use Ohm’s law)
- supernode required if indep. or dep. voltage source is connected between two nonreference nodes
o apply KCL to supernode (i.e., include currents flowing into/out of both nodes)
o the difference between the two node voltages in the supernode is equal to the
voltage source connecting them (this replaces the “missing” equation)
- N nodes lead to N−1 independent equations
- equations should have only node voltages as unknowns
Mesh analysis
- based on KVL applied to all “irreducible” meshes
- definition of mesh current: current assumed to circulate around a mesh, either
clockwise or counterclockwise
- interior circuit branches carry two mesh currents; their difference = actual current
- express voltages across resistors in terms of mesh currents (use Ohm’s law)
- supermesh required if indep. or dep. current source is shared between two meshes
o apply KVL to supermesh (i.e., sum up the voltages surrounding the
supermesh)
o the difference between the two mesh currents in the supermesh is equal to the
current source they share (this replaces the “missing” equation)
- N meshes lead to N independent equations
- equations should have only mesh currents as unknowns
Matrix equations
- used to express a system of simultaneous equations concisely
- standard form of expression
- matrix multiplication
o difference between pre- and post-multiplication
o no. of columns of left-hand matrix = no. of rows of right-hand matrix
o if m × n matrix pre-multiplies n × q matrix, result is m × q matrix
- Gaussian elimination (or Gauss-Jordan elimination)
o augmented matrix notation
o elementary row operations
o strive to put coefficient matrix into upper triangular form, then back-solve to
get solution to system
o if desired, can reduce coefficient matrix to identity matrix. “Right-hand-side”
matrix will then contain solution
- use of matrix inverse
Relevant course material:
HW:
Labs:
Textbook:
#1-#3
#1
Chaps. 1-3 except Secs. 3.6 and 3.7; Secs. 4.1-4.8; Mathcad document on matrix
equations; Appendix A
3