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**Problem**: Consider two conductors 1 and 2 made of the same ohmic material (ρ 1 = ρ2). Denote the length of the conductor by ℓ and the radius by r. The same voltage V is applied across the ends of both conductors. If r2 = 2 r1 , and ℓ2 = 2 ℓ1 , find the ratio I 2 / I1 of the currents.
1. I2 / I1 = 8
2. I2 / I1 = 1/2
3. I2 / I1 = 1
4. I2 / I1 = 1/4
5. I2 / I1 = 1/8
6. I2 / I1 = 2
7. I2 / I1 = 4

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###### Problem Details

Consider two conductors 1 and 2 made of the same ohmic material (ρ _{1} = ρ_{2}). Denote the length of the conductor by ℓ and the radius by r. The same voltage V is applied across the ends of both conductors. If r_{2} = 2 r_{1} , and ℓ_{2} = 2 ℓ_{1} , find the ratio I _{2} / I_{1} of the currents.

1. I_{2 }/ I_{1} = 8

2. I_{2 }/ I_{1} = 1/2

3. I_{2 }/ I_{1} = 1

4. I_{2 }/ I_{1} = 1/4

5. I_{2 }/ I_{1} = 1/8

6. I_{2 }/ I_{1} = 2

7. I_{2 }/ I_{1} = 4

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Based on our data, we think this problem is relevant for Professor Mestre's class at UIUC.