The SAME amount of current I passes through three different resistors. R2 has twice the cross-sectional area and the same length as R1, and R3 is three times as long as R1 but has the same cross-sectional area as R1. 1)In which case is the CURRENT DENSITY through the resistor the smallest

resistor R₂ has the lowest current density

Explanation:

The current density is

          j = I / A

now let's analyze each case

a) R₂ has an area 2A₀ and a length L₀ that R₁

b) R₃ has an area Ao and a length 3L₀ what R₁

we can see that all the area is given in relation to the resistance R₁

the current density in R₁ is

         j₁ = I / A₀

the current density in R₂

         j₂ = I / 2A₀

         j₂ 2 = ½ I/A₀

the current density in R₃

         j₃ = I / A₀

         j₂ < j₁ = j₃

therefore resistor R₂ has the lowest current density

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.

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