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The ratio of thermal conductivity of two rods $\mathrm{A}$ and $\mathrm{B}$ with the same area of cross-section is $3: 2$. If the thermal resistance of two rods is the same, then the ratio of length of rod A to length of rod B is
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$3: 2$
Given $A_1=A_2$ and $\frac{K_1}{K_2}=\frac{3}{2}$
If thermal resistance is equal
$R_1=R_2 \Rightarrow \frac{l_1}{K_1 A_1}=\frac{l_2}{K_2 A_2} \Rightarrow \frac{l_1}{l_2}=\frac{K_1}{K_2}=\frac{3}{2}$
If thermal resistance is equal
$R_1=R_2 \Rightarrow \frac{l_1}{K_1 A_1}=\frac{l_2}{K_2 A_2} \Rightarrow \frac{l_1}{l_2}=\frac{K_1}{K_2}=\frac{3}{2}$
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