A ring consisting of two parts ADB and ACB of same conductivity K carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperature `T_(1)` and `T_(2)` constant. The heat carried increases to 2H. What is should be the conductivity of the new ADB part?
(Given `(ACB)/(ADB)=3`)

Options

A. `(7)/(3)k`
B. `2`k
C. `(5)/(2)`k
D. `3`k

Answer

A

Explanation

`H=(T_(1)-T_(2))/(R)` and `2H = (T_(1)-T_(2))/(R) implies R' = (R)/(2)`
(where `R` &`R'` are thermal resistance).
`R = (1)/((L)/(kA) + (3L)/(kA)) implies R' = (1)/((kA)/(3L) + (k'A)/(3L)).`
`implies k' = (7k)/(3)` (k' = cond. Of `ADB` wire).