Calculating Current in a Mixed Tissue Conductor: A Weighted Average Approach

[ricebowl07]

The conductive tissues of the upper leg can be modeled as a 35-cm-long, 16-cm-diameter cylinder of muscle and fat. The resistivities of muscle and fat are 13 Ωm and 25 Ωm, respectively. One person's upper leg is 82% muscle, 18% fat. The resistivity of the whole leg will be a weighted average of the resistivities of muscle and fat. This is not the same as treating the system as two resistors (one made of muscle and the other of fat) in parallel; the muscle and fat are mixed together, not separate side by side.

Part A

What current is measured if a 1.9V potential difference is applied between the person's hip and knee?
Express your answer to two significant figures and include the appropriate units.

Relevant Equations

R = ρL/A
I = ΔV/R
A = ∏r^(2)

I kept getting 7.67 * 10^(-3) A for my answer. My attempt to solve this problem attached to this post.

 

[BvU]

Hello rice and welcome to PF.

I take it your question is: why is this wrong ?
Teachers instructions clearly state this is not the same as two resistors in parallel.

Teacher tells you to weigh the resistivities with percentage. Not the same as weighing 1/resisitivity by percentage !

 

[haruspex]

Just in case BvU's response is not completely clear to you...
You have added up the currents. Currents add up if the conductors are in parallel.
Similarly, you have taken the 18% and 82% as percentages of cross-sectional area. You should be taking them as percentages of length.