Three identical rods A, B and C are placed en | vedclass

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(A) Given that the rods are identical,let the length of each rod be $l$ and the cross-sectional area be $A_{area}$.Let $K_{A}, K_{B}, K_{C}$ be the th

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$\frac{1}{3} K_{A}$

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(A) Given that the rods are identical,let the length of each rod be $l$ and the cross-sectional area be $A_{area}$.Let $K_{A}, K_{B}, K_{C}$ be the thermal conductivities of rods $A, B, C$ respectively.According to the problem:$K_{B} = \frac{1}{2} K_{A}$$K_{B} = 3 K_{C} \implies K_{C} = \frac{K_{B}}{3} = \frac{K_{A}}{6}$Since the rods are connected in series,the equivalent thermal resistance $R_{eq}$ is the sum of individual resistances:$R_{eq} = R_{A} + R_{B} + R_{C}$$\frac{3l}{K_{eq} A_{area}} = \frac{l}{K_{A} A_{area}} + \frac{l}{K_{B} A_{area}} + \frac{l}{K_{C} A_{area}}$$\frac{3}{K_{eq}} = \frac{1}{K_{A}} + \frac{1}{K_{A}/2} + \frac{1}{K_{A}/6}$$\frac{3}{K_{eq}} = \frac{1}{K_{A}} + \frac{2}{K_{A}} + \frac{6}{K_{A}}$$\frac{3}{K_{eq}} = \frac{9}{K_{A}}$$K_{eq} = \frac{3 K_{A}}{9} = \frac{1}{3} K_{A}$

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