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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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

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