Consider the two insulating sheets with thermal resistance `R_(1)` and `R_(2)` as shown in figure. The temperature `theta` is

Options

A. `(theta_(1)theta_(2)R_(1)R_(2))/((theta_(1)+theta_(2))(R_(1)+R_(2)))`
B. `(theta_(1)R_(1)+theta_(2)R_(2))/(R_(1)+R_(2))`
C. `((theta_(1)+theta_(2))R_(1)R_(2))/(R_(1)^(2)+R_(2)^(2))`
D. `(theta_(1)R_(2) + theta_(2)R_(1))/(R_(1)+R_(2))`

Answer

D

Explanation

`H =(delta theta)/( R )`
is same through both sheets
`(theta - theta_(2))/( R_(2)) = (theta_(1) - theta)/(R_(1))`
`rArr`` theta R_(1) - theta_(2)R_(1) = theta_(1)R_(2) - theta R_(2)`
`rArr `` theta(R_(1) + R_(2)) = theta_(2)R_(1) + theta_(1) R_(2)`
`rArr`` theta =(theta_(2)R_(1) + theta_(1)R_(2))/(R_(1)+R_(2))`