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Find ratio of diameter of two Cylindrical Resistors?

  1. Feb 28, 2017 #1
    1. The problem statement, all variables and given/known data
    Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one(A) dissipates twice as much power as the other(B).

    Find ratio of dA/dB.
    2. Relevant equations
    P = VI = V2/R = I2R
    Area of cylinder = 2πrh + 2πr2

    3. The attempt at a solution
    I tried to find what the radius would be and managed to get 2 for A and 1 for B so r2 is 4 and 12 is 1 so 4/1, but that is wrong. I am confused on how to approach this problem.
     
  2. jcsd
  3. Feb 28, 2017 #2

    kuruman

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    The area that counts is the cross sectional area through which current flows.
     
  4. Feb 28, 2017 #3
    Ok so only the 2πr2? What do I do to figure out the ratio with double the power for A over B?
     
  5. Feb 28, 2017 #4

    kuruman

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    No. The resistance of a cylindrical conductor is
    $$R=\frac{\rho L}{A}$$ where ρ = resistivity, L = length and A = cross sectional area = πr2. For each resistor, write expressions for the resistance and power, then take the ratio of the powers.
     
  6. Feb 28, 2017 #5
    Oh, ok so I get P = V2/R = V2/(ρL/πr2) for B and thus A is V2/(ρL/2πr2). Correct?
     
  7. Mar 1, 2017 #6

    kuruman

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    Correct.
     
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