 # Lecture 5 Review: Circuit reduction Related educational modules:

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Lecture 5 Review: Circuit reduction Related educational modules:
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:

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.)