Three rods of same dimensions have thermal condutivity `3K,2K` and `K` They are arranged as shown in Then the temperature of the junction in steady state is
.

Options

A. `75^(@)C`
B. `(200)/(3).^(@)C`
C. `40^(@)C`
D. `(100)/(3).^(@)C`

Answer

B

Explanation

(2) `R = (1)/("Thermal conductivity")`
`R_(1) = (R )/(3), R_(2) = (R )/(2), R_(3) = R`
`i = i_(1) + i_(2)`
`(100 - theta)/(R//3) = (theta - 50)/(R//2) + (theta - 0)/(R )`
`300 - 3 theta = 2 theta - 100 + theta`
`6 theta = 400 implies theta = (200)/(2).^(@)C`