Download review for elec 105 midterm exam #1 (fall 2001)

ELEC 225
Circuit Theory I
Fall 2005
Review Topics for Exam #2
 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. You
should be familiar with the topics on the previous review sheet in addition to those listed below.
Nodal analysis
- based on KCL applied to all nodes except reference node
- definition of node: not just a “dot;” includes wires connected to dot(s)
- 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 makes up for the “missing” equation)
- N nodes lead to N−1 independent equations
- equations should have only node voltages as unknowns
- in general, the solution of a system of simultaneous equations is required (for N
nodes, it’s N−1 equations in N−1 unknowns)
Mesh analysis
- based on KVL applied to all “irreducible” meshes
- definition of mesh
- definition of mesh current: current assumed to circulate around a mesh, either
clockwise or counterclockwise
- interior circuit branches carry two mesh currents which combine linearly
- 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 makes up for the “missing” equation)
- N meshes lead to N independent equations
- equations should have only mesh currents as unknowns
- in general, the solution of a system of simultaneous equations is required (for N
meshes, it’s N equations in N unknowns)
Thévenin and Norton equivalent circuits
- TEC and/or NEC is associated with a specific set of terminals; a different set of
terminals in the same circuit has a different TEC/NEC
- open-circuit voltage (voc) appears at terminals with external circuit removed
- short-circuit current (isc) flows through short between terminals
- polarity of voc vs. direction of isc
- Thévenin voltage (vth) = voc
- Norton current (iN) = isc
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Thévenin and Norton equivalent resistance, Rth = RN = voc / isc = vth / iN
Thévenin (Norton) resistance can be found via three possible methods:
o Find voc and isc and then evaluate the ratio Rth = RN = voc / isc
o If no dependent sources are present, deactivate all independent sources
(replace voltage sources with shorts and current sources with opens), and find
Req of the circuit using series/parallel combination formulas
o If dependent sources are present, deactivate all independent sources, apply a
test source (vt or it), and evaluate the ratio Rth = RN = vt / it
Source transformations
- any voltage source in series with a resistor is equivalent to a current source in parallel
with a resistor (transforms a TEC to an NEC)
- any voltage source in series with a resistor is equivalent to a current source in parallel
with a resistor (transforms an NEC to a TEC)
Maximum power transfer
- if load resistance (RL) is controllable, set RL = Rth
- if Thévenin resistance (Rth) is controllable, set Rth = 0 (or as small as possible)
- if RL = Rth (only!), power delivered to load is PL = (vth2)/(4Rth)
- trade-off between maximum power transfer and efficiency
- if RL = Rth, then percentage power delivered to load can never be more than 50% and
is usually much less than 50%
Superposition and linearity
- principle of superposition: Any voltage or current in a circuit is a weighted sum of
the contributions from the individual sources driving the circuit. Put another way,
any voltage or current in circuit can be expressed as a linear combination of the
individual sources driving the circuit.
- superposition only applies if all components have linear voltage-to-current
relationships. These kinds of components include:
o all independent sources (voltage or current)
o resistors
o dependent sources (voltage or current) with constant gain
- procedure to apply superposition:
o activate one independent source at a time; deactivate all others (i.e., replace
indep. voltage sources with shorts and indep. current sources with opens)
o leave dependent source alone
o find desired voltage(s) and/or current(s) due to the active source
o repeat the above for each individual independent source in the circuit
o add together the components of the desired voltage(s) and/or current(s) due to
the individual sources to find the actual (total) voltage(s) and/or currents(s)
Relevant course material:
HW:
Labs:
Textbook:
#5-#7
#3-#4
All of Chap. 4
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