A composite rod is made of three rods of equa | vedclass

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(A) For rods connected in series,the equivalent thermal resistance $R_{eq}$ is the sum of individual thermal resistances: $R_{eq} = R_1 + R_2 + R_3$.G

Vedclass · Accepted Answer

$15K/16$

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(A) For rods connected in series,the equivalent thermal resistance $R_{eq}$ is the sum of individual thermal resistances: $R_{eq} = R_1 + R_2 + R_3$.Given that all rods have equal length $l$ and cross-sectional area $A$,the thermal resistance of a rod is $R = \frac{l}{KA}$.Thus,the equivalent thermal resistance is:$R_{eq} = \frac{l}{(K/2)A} + \frac{l}{(5K)A} + \frac{l}{KA} = \frac{l}{A} \left( \frac{2}{K} + \frac{1}{5K} + \frac{1}{K} ight)$.Simplifying the expression inside the bracket:$R_{eq} = \frac{l}{A} \left( \frac{10 + 1 + 5}{5K} ight) = \frac{l}{A} \left( \frac{16}{5K} ight) = \frac{16l}{5KA}$.For the composite rod of total length $3l$,the equivalent thermal conductivity $K_{eq}$ is given by:$R_{eq} = \frac{3l}{K_{eq}A} = \frac{16l}{5KA}$.Solving for $K_{eq}$:$K_{eq} = \frac{3 	imes 5K}{16} = \frac{15K}{16}$.

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