Question

Figure shown below represents, parallel combination of two metallic slabs of same thickness having area of cross sections $2{\text{m}}^2$ and $3{\text{m}}^2$ respectively, connected to the same temperature difference. If the thermal conductivities of each slab is $300{\text{W/m}}^{\circ }\text{C}$, then equivalent thermal conductivity is (in ${\text{W/m}}^{\circ }\text{C}$)

• A. $500$
• B. $250$
• C. $300$
• D. $350$

Answer 1

The correct option is C $300$

Given,
$l_1=l_2=l;A_1=2{\text{m}}^2;A_2=3{\text{m}}^2$
Thermal conductivity of each slab $\left(k\right)=300{\text{W/m}}^{\circ }\text{C}$
Equivalent thermal conductivity $\left(k\right)=\frac{k_1{A}_1+k_2{A}_2}{A_1+A_2}$
$=\frac{k(A_1+A_2)}{A_1+A_2}$
$=300{\text{W/m}}^{\circ }\text{C}$