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 . Step 1Combine resistors R4 and R5 to form equivalent resistance R4,5. This is a series combination, so: R4,5 = R4 + R5 Step 2Combine R3 and the equivalent resistance R4,5. These resistances are connected in parallel, so: R3,4,5 = R3 || R4,5 Step 3Combine 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 Step 4Finally, combine R1and R2,3,4,5. These are connected in parallel, so: R1,2,3,4,5 = R1 || R2,3,4,5 Example 2 Systematically reduce this combination circuit to a single equivalent-value resistor. Step 1Combine resistors R4 and R5 to form equivalent resistance R4,5. This is a parallel combination, so: R4,5 = R4 || R5 Step 2Combine R3 and the equivalent resistance R4,5. These resistances are connected in series, so: R3,4,5 = R3 + R4,5 Step 3Combine 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 Step 4Finally, combine R1and R2,3,4,5. These are connected in series, so: R1,2,3,4,5 = R1 + R2,3,4,5