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Lecture 4
•Review:
•KVL, KCL
•Circuit analysis examples
•Series, parallel circuit elements
•Related educational modules:
–Section 1.4, 1.5
Review: KVL & KCL
• KVL: algebraic sum of all voltage differences around
any closed loop is zero
N
v
k 1
k
(t )  0
• KCL: algebraic sum of all currents entering a node is
zero
N
i
k 1
k
(t )  0
Review: Circuit analysis
• General circuit analysis approach:
• Assign element voltages, currents according to passive
sign convention
• Apply KVL, KCL, and voltage-current relations as
necessary to solve for desired circuit parameters
• The general idea is to write as many equations as you
have unknowns, and solve for the desired unknowns
Circuit analysis – example 1
• For the circuit below, determine: vAC, vX, vDE, RX, and the
power absorbed by the 2 resistor
Example 1 – continued
• Talk about open circuit, short circuit
terminology
Circuit analysis tips
• There are (generally) multiple ways to do a problem
• Some time spent examining the problem may be
productive!
• Subscript notation on voltages provides desired
polarity
• It may not be necessary to determine all voltages in
a loop in order to apply KVL
• The circuit does not need to be physically closed in
order to apply KVL
More circuit analysis tips
• KVL through a current source is generally not
directly helpful
• Get another equation, but the voltage across a current
source is not defined  additional unknown introduced
• KCL next to a voltage source generally not directly
helpful
• Get another equation, but the voltage across a current
source is not defined  introduce an additional unknown
Circuit analysis – example 2
• Determine the voltages across both resistors.
Example 2 – continued
•
Circuit analysis – example 3
• We have a “dead” battery, which only provides 2V
• Second battery used to “charge” the dead battery – what
is the current to the dead battery?
Non-ideal voltage source models
• Add a “source
resistance” in series
with an ideal voltage
source
• We will define the term
series formally later
Non-ideal current source models
• Add a “source
resistance” in parallel
with an ideal current
source
• We will define the term
parallel formally later
Example 3 – revisited
• Our battery charging example can now make sense
• Include internal (source resistances) in our model
Ideal sources can provide infinite power
• Connect a “load” to an ideal voltage source:
• Be sure to discuss previous results relative to
open, short-circuit expectations
Non-ideal sources limit power delivery
• “Loaded” non-ideal voltage source
• Validate previous result with open, shortcircuit discussion.
Ideal sources can provide infinite power
• Connect a “load” to an ideal current source:
• Be sure to discuss previous results relative to
open, short-circuit expectations
Non-ideal sources limit power delivery
• “Loaded” non-ideal current source
• Validate previous results with open vs. short
circuit discussion.
When are ideal source models “good enough”?
• Ideal and non-ideal voltage sources are the “same” if RLoad >> RS
vLoad
 RLoad
 VS 
 RS  RLoad




vLoad  VS if RLoad  RS
• Ideal and non-ideal current sources are the “same” if RLoad << RS
iLoad

RS
 I S 
 RS  RLoad




iLoad  I S if RLoad  RS
Series and parallel circuit elements
• Circuit elements are in series if all elements carry
the same current
• KCL at node “a” provides i1 = i2
Series and parallel circuit elements
• Circuit elements are in parallel if all elements have
the same voltage difference
• KVL provides v1 = v2
Circuit reduction
• In some cases, series and parallel combinations of
circuit elements can be combined into a single
“equivalent” element
• This process reduces the overall number of
unknowns in the circuit, thus simplifying the circuit
analysis
• Fewer elements  fewer related voltages, currents
• The process is called circuit reduction