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Lesson 6: More Examples of Reducing Complicated Circuits

Here are two examples of circuits having five resistors.

Example 1

Reduce this circuit to a single resistance--one step at a time--through a series of equivalent resistances

.fig05112112.gif (2012 bytes)

Step 1

Combine resistors R4 and R5 to form equivalent resistance R4,5.

This is a series combination, so:

R4,5 = R4 + R5

 

fig05112113.gif (1964 bytes)
Step 2

Combine R3 and the equivalent resistance R4,5.

These resistances are connected in parallel, so:

R3,4,5 = R3 || R4,5

 

fig05112114.gif (1788 bytes)
Step 3

Combine R2 and equivalent resistance R3,4,5 to form the equivalent, R2,3,4,5:

These resistances are connected in series, so:

R2,3,4,5 = R2 + R3,4,5

 

fig05112115.gif (1712 bytes)
Step 4

Finally, combine R1and R2,3,4,5.

These are connected in parallel, so:

R1,2,3,4,5 = R1 || R2,3,4,5

 

fig05112116.gif (1483 bytes)

 

Example 2

Systematically reduce this combination circuit to a single equivalent-value resistor.

fig05112117.gif (2039 bytes)

Step 1

Combine resistors R4 and R5 to form equivalent resistance R4,5.

This is a parallel combination, so:

R4,5 = R4 || R5

fig05112118.gif (1865 bytes)
Step 2

Combine R3 and the equivalent resistance R4,5.

These resistances are connected in series, so:

R3,4,5 = R3 + R4,5

fig05112119.gif (1845 bytes)
Step 3

Combine R2 and equivalent resistance R3,4,5 to form the equivalent, R2,3,4,5:

These resistances are connected in parallel, so:

R2,3,4,5 = R2 || R3,4,5

fig05112120.gif (1604 bytes)
Step 4

Finally, combine R1and R2,3,4,5.

These are connected in series, so:

R1,2,3,4,5 = R1 + R2,3,4,5

 

fig05112116.gif (1483 bytes)


Author and content provider: David L.Heiserman
Publisher: SweetHaven Publishing Services

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