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Resistance in Series and Parallel Connections

Worked Examples on Resistance in Series and Parallel Connections

Example 1: Series Connection

Three resistors, R1 = 4Ω, R2 = 6Ω, and R3 = 10Ω, are connected in series. Find the total resistance.

Solution: Rtotal = R1 + R2 + R3 = 4 + 6 + 10 = 20Ω

Series Connection Diagram

Example 2: Parallel Connection

Three resistors, R1 = 6Ω, R2 = 12Ω, and R3 = 18Ω, are connected in parallel. Find the total resistance.

Solution: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 = 1/6 + 1/12 + 1/18

1/Rtotal = 6/36 = 1/6, so Rtotal = 6Ω

Parallel Connection Diagram

Example 3: Series Connection

Two resistors, R1 = 15Ω and R2 = 10Ω, are connected in series. Find the total resistance.

Solution: Rtotal = R1 + R2 = 15 + 10 = 25Ω

Series Connection Diagram

Example 4: Parallel Connection

Two resistors, R1 = 8Ω and R2 = 16Ω, are connected in parallel. Find the total resistance.

Solution: 1/Rtotal = 1/R1 + 1/R2 = 1/8 + 1/16 = 2/16 + 1/16 = 3/16

Rtotal = 16/3 = 5.33Ω

Parallel Connection Diagram

Example 5: Series Connection

Four resistors, R1 = 2Ω, R2 = 3Ω, R3 = 4Ω, and R4 = 5Ω, are connected in series. Find the total resistance.

Solution: Rtotal = R1 + R2 + R3 + R4 = 2 + 3 + 4 + 5 = 14Ω

Series Connection Diagram

Example 6: Parallel Connection

Three resistors, R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω, are connected in parallel. Find the total resistance.

Solution: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 = 1/10 + 1/20 + 1/30

1/Rtotal = 6/60 = 1/10, so Rtotal = 10Ω

Parallel Connection Diagram

Example 7: Series Connection

Two resistors, R1 = 7Ω and R2 = 9Ω, are connected in series. Find the total resistance.

Solution: Rtotal = R1 + R2 = 7 + 9 = 16Ω

Series Connection Diagram

Example 8: Parallel Connection

Two resistors, R1 = 5Ω and R2 = 15Ω, are connected in parallel. Find the total resistance.

Solution: 1/Rtotal = 1/R1 + 1/R2 = 1/5 + 1/15 = 3/15 + 1/15 = 4/15

Rtotal = 15/4 = 3.75Ω

Parallel Connection Diagram

Example 9: Mixed Connection

Two resistors, R1 = 12Ω and R2 = 6Ω, are connected in parallel. The combination is then connected in series with R3 = 8Ω. Find the total resistance.

Solution: First, find Rparallel: 1/Rparallel = 1/R1 + 1/R2 = 1/12 + 1/6 = 1/4

Rparallel = 4Ω. Total resistance: Rtotal = Rparallel + R3 = 4 + 8 = 12Ω

Mixed Connection Diagram

Example 10: Mixed Connection

Three resistors, R1 = 9Ω, R2 = 12Ω, and R3 = 18Ω, are connected in parallel. The combination is then connected in series with R4 = 10Ω. Find the total resistance.

Solution: First, find Rparallel: 1/Rparallel = 1/R1 + 1/R2 + 1/R3 = 1/9 + 1/12 + 1/18

1/Rparallel = 6/36 = 1/6, so Rparallel = 6Ω. Total resistance: Rtotal = Rparallel + R4 = 6 + 10 = 16Ω

Mixed Connection Diagram

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