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In a composite rod, when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined from end to end then if $K$ is the effective coefficient of thermal conductivity, the value of $(l_1 + l_2)/K$ is
$\frac{{{l_1}}}{{{K_1}}} + \frac{{{l_2}}}{{{K_2}}}$
$\frac{{{l_1}}}{{{K_2}}} + \frac{{{l_2}}}{{{K_1}}}$
$\frac{{{l_1}}}{{{K_1}}} - \frac{{{l_2}}}{{{K_2}}}$
$\frac{{{l_1}}}{{{K_2}}} - \frac{{{l_2}}}{{{K_1}}}$
Solution
Guven that
$k$ is coetficient of thermal conductivity $\frac{l_1+l_2}{k}=?$
As ux know formala heat current
$d q=K \cdot A \frac{(d T)}{L}=\frac{d T}{d q}=\frac{L}{K \cdot A}$
As we know electricity current
$d v=(R) d i$
$\frac{d v}{d i}=R$
Thermal resistance $R=\frac{d}{k A}$
as per our thermal conductivity $=\frac{l_1+l_2}{k}$
Thormal resistance is $\frac{l l}{K_1}=\frac{l_2}{k_2}$
