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azaharak
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One of the textbooks I've stumbled across states that the radial resistance of a coaxial cable ( current running from inner cylinder to outer cylinder via silicon in between) is given byR = [resistivity * natural log of (b/a)] / [2*pi()*(length of cable)]
where b is the outer radii and a is the inner radiiThe derivation was given as dR= resistivity*dr / A and then integrated from a to b.My question/issue is the dependence of the area on the radial length, I'm not so sure about the correctness of the differential form above.
If you follow through the chain rule with A a function of r
dR/dr= resistivity/Area + (d/dA)*(resistivity*r/Area)*(dA/dr)
which becomes
dR/dr= resistivity/area -[resistivity*r/(Area^2)] * (2*pi()*L)
which becomes
dR/dr=resistivity/area - resistivity/area =0
meaning that the resistance is a constant value which should be
R = resistivity / (2*Pi*L ) where L is the length of the cable (constant)
Help! Thank you very much.Thank you!
where b is the outer radii and a is the inner radiiThe derivation was given as dR= resistivity*dr / A and then integrated from a to b.My question/issue is the dependence of the area on the radial length, I'm not so sure about the correctness of the differential form above.
If you follow through the chain rule with A a function of r
dR/dr= resistivity/Area + (d/dA)*(resistivity*r/Area)*(dA/dr)
which becomes
dR/dr= resistivity/area -[resistivity*r/(Area^2)] * (2*pi()*L)
which becomes
dR/dr=resistivity/area - resistivity/area =0
meaning that the resistance is a constant value which should be
R = resistivity / (2*Pi*L ) where L is the length of the cable (constant)
Help! Thank you very much.Thank you!
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