If two metallic plates of equal thicknesses and thermal conductiv… - Vidyadip

MCQ

If two metallic plates of equal thicknesses and thermal conductivities ${K_1}$ and ${K_2}$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

A
$\frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}$
✓
$\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
C
$\frac{ K _{1}+ K _{2}}{2 K _{1} K _{2}}$
D
$\frac{ K _{1}+ K _{2}}{ K _{1} K _{2}}$

✓

Answer

Correct option: B.

$\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$

b
(b) In series ${R_{eq}} = {R_1} + {R_2}$

==> $\frac{{2l}}{{{K_{eq}}A}} = \frac{l}{{{K_1}A}} + \frac{l}{{{K_2}A}}$

==> $\frac{2}{{{K_{eq}}}} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}}$

==> ${K_{eq}} = \frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$

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