The cross-section area and length of cylindrical conductor are A and l respectively. The specific conductivity varies as σ(x)=σ0lx ,where x is the distance along the axis of the cylinder from one of its ends. Compute the resistance of the system along the cylindrical axis

Resistance of thin elementary disc is dR=ρdxA=1σdxA=xσoldxA Rtotal=1σolA∫0lx1/2dx=1σolAl3/23/2=23lAσo

The cross-section area and length of cylindrical conductor are A and l respectively. The specific conductivity varies as σ(x)=σ0lx ,where x is the distance along the axis of the cylinder from one of its ends. Compute the resistance of the system along the cylindrical axis

Resistance of thin elementary disc is dR=ρdxA=1σdxA=xσoldxA Rtotal=1σolA∫0lx1/2dx=1σolAl3/23/2=23lAσo

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The cross-section area and length of cylindrical conductor are $A$ and $l$ respectively. The specific conductivity varies as $σ (x) = σ_{0} \frac{l}{\sqrt{x}}$ ,where x is the distance along the axis of the cylinder from one of its ends. Compute the resistance of the system along the cylindrical axis

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$\frac{2 \sqrt{l}}{3 A σ_{o}}$

$\frac{3 \sqrt{l}}{2 A σ_{o}}$

$\frac{2 l}{3 A σ_{o}}$

$\frac{\sqrt{l}}{A σ_{o}}$

answer is C.

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Resistance of thin elementary disc is
$d R = \frac{ρ d x}{A} = \frac{1}{σ} \frac{d x}{A} = \frac{\sqrt{x}}{σ_{o} l} \frac{d x}{A}$

$R_{t o t a l} = \frac{1}{σ_{o} l A} \int_{0}^{l} x^{1 / 2} d x = \frac{1}{σ_{o} l A} \frac{l^{3 / 2}}{3 / 2} = \frac{2}{3} \frac{\sqrt{l}}{A σ_{o}}$

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The cross-section area and length of cylindrical conductor are A and l respectively. The specific conductivity varies as σ(x)=σ0lx ,where x is the distance along the axis of the cylinder from one of its ends. Compute the resistance of the system along the cylindrical axis

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