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Two rods with the same dimensions have thermal conductivities in the ratio $1 : 2$ . They are arranged between heat reservoirs with the same temperature difference, in two different configurations, $A$ and $B$ . The rates of heat flow in $A$ and $B$ are $I_{A}$ and $I_{B}$ respectively. The ratio $\frac{I_{A}}{I_{B}}$ is equal to

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$1 : 2$

$1 : 3$

$2 : 5$

$2 : 9$

answer is D.

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Detailed Solution

Rate of heat flow, $H \propto \frac{T D}{R}$

$∴ T D =$ temperature difference is same.

$∴ H \propto \frac{1}{Thermal resistance}$ $\frac{H_{A}}{H_{B}} = \frac{R_{B}}{R_{A}} = \frac{(R) (2 R) / (R + 2 R)}{(R + 2 R)} = \frac{2}{9}$

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