Two slabs A and B of different materials but of the same thickness are joined as shown in figure. The thermal conductivities of A and B are $k_{1} a n d k_{2}$ respectively. The thermal conductivity of the composite slab will be

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Solution

The correct option is D

The thermal resistance of a slab of length l,area A and thermal conductivity kis given by

$R = \frac{l}{k A} F o r s l a b A : R_{1} = \frac{\frac{1}{2}}{k_{1} A} F o r s l a b B : R_{2} = \frac{\frac{1}{2}}{k_{2} A}$

Since the slabs are joined in series, the thermal resistance of the composite slab is

$R_{c} = R_{1} + R_{2}$

$O r \frac{1}{k_{c} A} = \frac{\frac{1}{2}}{k_{1} A} + \frac{\frac{1}{2}}{k_{2} A} O r \frac{1}{k_{c}} = \frac{1}{2} (\frac{1}{k_{1}} + \frac{1}{k_{2}}) W h i c h g i v e s k_{c} = \frac{2 k_{1} k_{2}}{(k_{1} + k_{2})}$

Hence the correct choice is (d).

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