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Lecture 5
•Review:
•Series, parallel circuit elements
•Circuit reduction
•Related educational modules:
–Section 1.5
Review: series and parallel circuit elements
• Elements in series if they have the same current
• Elements in parallel have the same voltage
Circuit reduction
• Some circuit problems can be simplified by
combining elements to reduce the number of
elements
• Reducing the number of elements reduces the number of
unknowns and thus the number of equations which must
be written to determine these unknowns
Series circuit elements – example 1
• Apply KCL at any node  all elements have the same current
• All of the above circuit elements are in series
Series element circuit reduction – example 1

• KVL around the loop:
-V1 + i·R1 + V2 + i·R2 + i·R3 – V3 + i·R4 = 0
(-V1 + V2– V3) + i(R1 + R2 + R3 + R4) = 0
Series circuit reduction
• Notes:
• Voltage sources in series add directly to form an
equivalent voltage source
• Resistances in series add directly to form an equivalent
resistance
Series circuit reduction – Example 2
• Determine the power delivered by the 20V source
Voltage Division
• Series combination of N resistors:
i
+
Vk
-
Voltage Divider Formula
• Ratio of VK to the total voltage is the same as the ratio of RK
to the total series resistance
Voltage Dividers – special case
• Voltage source in series with two resistors:
Voltage division – example 1
• Determine the power dissipated by the 2 resistor
Voltage division – example 2
• Determine the voltage V1 in the circuit below.
Parallel circuit elements – example 1
• Apply KVL around any loop  all elements have the
same voltage
• All of the above circuit elements are in parallel
Parallel element circuit reduction – example 1

• KCL at upper node:
Parallel circuit reduction
• Notes:
• Current sources in parallel add directly to form an
equivalent current source
• Definition: Conductance is the inverse of resistance


• Units are siemens or mhos (abbreviated S or
)
• Conductances in parallel add directly to form an
equivalent conductance
• Go back to previous example, look at it in
terms of conductances
Parallel element circuit example 1 – revisted
Parallel circuit reduction – Example 2
• Determine the power delivered by the 2A source
Current Division
• Parallel combination of N resistors:
Current Divider Formula
• Ratio of iK to the total current is the same as the ratio of GK
to the total parallel conductance
Current Divider – special case
• Current source in parallel with two resistors

Current division – example 1
• Determine the current in the 2 resistor
Current division – example 2
• Determine the value of R which makes i = 2mA
Circuit Reduction
• Series and parallel combinations of circuit elements
can be combined into a “equivalent” elements
• The resulting simplified circuit can often be
analyzed more easily than the original circuit
Circuit Reduction – example 1
• Determine the current in the 2 resistor. (Note: we wrote
the governing equations for this example in lecture 3.)