Lesson 5: Examples of Reducing  More Complicated Circuits

Example 1

The total resistance of this circuit can be expressed as:

RT = R1 + R2 || (R3 + R4)

The objective of this example is to reduce this circuit to a single resistance--one step at a time--through a series of equivalent resistances.

Step 1:

Combine resistances R3 and R4 to form equivalent resistance R3,4.

These two resistors are in series, so:

R3,4 = R3 + R4

Step 2:

Combine R2 with the equivalent resistance R3,4 to form R2,3,4.

These resistances are in parallel, so:

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

Step 3:

Combine resistances R1 and R2,3,4 to form equivalent resistance R1,2,3,4.

These resistances are connected in series, so:

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

 Note Students often ask, "How do we know where to start?" or "How do we know what to do next?" The answer is simple: Do whatever you can do.  Where you find two resistors connected in series or in parallel with one another, combine those two values. Then you will find two more that can be combined--do that next. (And don't try to memorize a pattern for working out these equivalent circuits.)

Example 2

Here is another example of a four-resistor circuit.

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

Step 1:

Combine resistors R3 and R4 to yield equivalent resistance R3,4.

These two resistors are connected in parallel, so:

R3,4 = R3 || R4

Step 2:

Combine resistor R2 and equivalent resistance R3,4 to produce equivalent resistanceR2,3,4 .

These resistances are connected in series, so:

R2,3,4 = R2 + R3,4

Step 3:

Combine resistances R1 and R2,3,4 to finish the reduction procedure.

The resistances in this instance are connected in parallel, so:

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