   Chapter 18, Problem 46AP

Chapter
Section
Textbook Problem

How many different resistance values can be constructed from a 2.0-Ω, a 4.0-Ω, and a 6.0-Ω resistor? Show how you would get each resistance value either individually or by combining them.

To determine
The number of possible distinct combination of resistances.

Explanation

The distinct combinations are -

• Connecting a single resistor: This will give three values - R1=2.00Ω , R2=4.00Ω and R3=6.00Ω .
• R1 and R2 in parallel:

R4=R1R2R1+R2=(2.00Ω)(4.00Ω)(2.00Ω)+(4.00Ω)=1.33Ω

• R1 and R3 in parallel:

R5=R1R3R1+R3=(2.00Ω)(6.00Ω)(2.00Ω)+(6.00Ω)=1.5Ω

• R2 and R3 in parallel:

R6=R2R3R2+R3=(4.00Ω)(6.00Ω)(4.00Ω)+(6.00Ω)=2.4Ω

• R2 and R3 in series:

R7=R2+R3=(4.00Ω)+(6.00Ω)=10Ω

• R1 and R3 in series:

R8=R1+R3=(2.00Ω)+(6.00Ω)=8Ω

• R1 , R2 and R3 in series:

R9=R1+R2+R3=(2.00Ω)+(4.00Ω)+(6.00Ω)=12Ω

• R1 , R2 and R3 in parallel:

1R10=1R1+1R2+1R3=12.00Ω+14.00Ω+16.00Ω

On Re-arranging,

R10=1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 