Find ratio of diameter of two Cylindrical Resistors?

[jlmccart03]

Homework Statement

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.

Homework Equations

P = VI = V²/R = I²R
Area of cylinder = 2πrh + 2πr²

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.

 

[kuruman]

The area that counts is the cross sectional area through which current flows.

 

[jlmccart03]

The area that counts is the cross sectional area through which current flows.

Ok so only the 2πr²? What do I do to figure out the ratio with double the power for A over B?

 

[kuruman]

Ok so only the 2πr²

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.

 

[jlmccart03]

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.

Oh, ok so I get P = V²/R = V²/(ρL/πr²) for B and thus A is V²/(ρL/2πr²). Correct?

 

[kuruman]

Correct.