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Two bars of equal length and the same cross-sectional area but of different thermal conductivities, \( k_{1} \) and \( k_{2} \), are joined end to end as shown in figure-4.36. One end of the composite bar is maintained at temperature \( T_{h} \) whereas the opposite end is held at \( T_{c} \).

If there are no heat losses from the sides of the bars, the temperature \( T_{j} \) of the junction is given by :
(A) \( \frac{k_{2}}{k_{1}} \frac{\left(T_{h}+T_{c}\right)}{2} \)
(B) \( \frac{k_{2}}{k_{1}+k_{2}}\left(T_{h}+T_{c}\right) \)
(C) \( \frac{k_{1}+k_{2}}{k_{2}} \frac{\left(T_{h}+T_{c}\right)}{2} \)
(D) \( \frac{1}{k_{1}+k_{2}}\left(k_{1} T_{h}+k_{2} T_{c}\right) \)
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