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Series and Parallel Combination of Resistors

A hollow cyli...

Question

A hollow cylinder has length L, inner radius $r_{1}$ , outer radius $r_{2}$ , and thermal conductivity k. The thermal resistance of the cylinder for radial conduction is

\frac{l n (r_{2} / r_{1})}{2 π k L}

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\frac{l n (r_{1} / r_{2})}{2 π k L}

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\frac{2 π k L}{l n (r_{2} / r_{1})}

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\frac{2 π k L}{l n (r_{1} / r_{2})}

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Solution

The correct option is A $\frac{l n (r_{2} / r_{1})}{2 π k L}$
$Q = \frac{Δ T}{T h e r m a l r e s i s t a n c e}$

Thermal resistance = $\int_{r_{1}}^{r_{2}} \frac{l}{k A} = \int_{r_{1}}^{r_{2}} \frac{d r}{k \times 2 π r L}$

$= \frac{d r}{2 π L k} \int_{r_{1}}^{r_{2}} \frac{d r}{r} = \frac{1.}{2 π L k} [l n r]_{r_{1}}^{r_{2}} = \frac{1}{2 π L k} l n \frac{r_{2}}{r_{1}}$

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