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Resistance problem- combination circuit

  1. Apr 29, 2008 #1

    adv

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    Question 3. Find the total resistance of the following circuit.

    Formulas:

    R= V/I

    If the # of resistors connected in series is n, the equiv. resistor is given by
    Rs = R1 + R2 +... + Rn

    likewise with resistors connected in parallel,
    1/Rp = 1/R1 + 1/R2 +... + 1/Rn

    Given:
    V0 = 120 V
    R1 = 20 Ω
    R2 = 22 Ω
    R3 = 30 Ω
    R4 = 27 Ω
    R5 = 40 Ω
    R6 = 20 Ω
    R7 = 20 Ω

    My attempt:

    Applying Ohm’s Law to the entire circuit:

    I0 = V0 / RT , where RT is the total resistance in the circuit

    But since R3 and R4 are connected in series,

    RS = R3 + R4
    = 30 Ω + 27 Ω
    = 57 Ω

    Then RT1 and R7 are connected in parallel:

    1/RP = 1/RS + 1/R7
    = 1/57 + 1/20
    = 20/1140 + 57/1140
    = 77/1140 Ω
    RP = 14.8 Ω
    = 15 Ω

    Solve five resistors R1, R2, RP, R5 and R6. These resistors are connected in series

    RT = R1 + R2 + R3 + R4 + R5 + R6
    = 20 Ω + 22 Ω + 15 Ω + 40 Ω + 20 Ω
    = 117 Ω

    Therefore, the total resistance of the circuit is 117 Ω.

    I'm not sure I took the right approach. Any help would be appreciated. Thanks.
     

    Attached Files:

  2. jcsd
  3. Apr 30, 2008 #2
    R2 and R5 are in series with R3 and R4. They should be included in the calculation of RS.
     
  4. Apr 30, 2008 #3
    R2, R3, R4, and R5 are all in series

    R8=R2+R3+R4+R5

    R8 is parrallel to R7

    1/R9=1/R8 + 1/R7

    R9 is in series with R1 and R6

    RTotal=R1+R9+R6
     
  5. Apr 30, 2008 #4

    adv

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    Here is the correction:

    Since R2, R3, R4 and R5 are connected in series,

    R8 = R2 + R3 + R4 + R5
    = 22 Ω + 30 Ω + 27 Ω + 40 Ω
    = 119 Ω

    Then R7 and R8 are connected in parallel:

    1/R9 = 1/R7 + 1/R8
    = 1/20 + 1/119
    = 119/2380 + 20/2380
    = 139/2380 Ω
    R9 = 17.1 Ω
    = 17 Ω

    Solve three resistors R1, R9 and R6. These resistors are connected in series

    RT = R1 + R9 + R6
    = 20 Ω + 17 Ω + 20 Ω
    = 57 Ω

    Therefore the total resistance of the circuit is 57 Ω.

    I think this is correct now. Thank you Phlogistonian and Drdizzard. BTW, the relabeling of R8 and R9 was less confusing than Rs and Rp. I guess it was more consistant. Anywho, thanks!
     
  6. Apr 30, 2008 #5
    That's correct the total resistance of the circuit is 57 ohms. I am glad I was able to help.
     
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