Three identical rods of length 1 m each, having cross-sectional area of `1cm^2` each and made of aluminium, copper and steel, respectively, are maintained at temperatures of `12^@C`,`4^@C` and `50^@C`, respectively, at their separate ends. Find the teperature of their common junction.
`[K_(Cu)=400 W//m-K,K_(Al)=200 W//m-K,K_("steel")=50 W//m-K]`

Explanation

`R_(AI) = (L)/(KA) = (1)/(10^(-4)xx200) = (10^(4))/(200)`
Similarly `R_(stell) = (10^(4))/(50)` and `R_(copper) = (10^(4))/(400)`
Let temperature of common junction `= T` then from Kirchoff's current laws,
`i_(AI) +i_(steel) +i_(Cu) = 0`
`rArr (T-12)/(R_(AI)) +(T-50)/(R_(steel)) +(T-4)/(R_(Cu)) = 0`
`rArr (T-12) 200 +(T - 50) 50 +(T-4) 400`
`rArr 4(T-12) +(T-50) +8(T-4) = 0`
`rArr 13T = 48 +50 +32 = 130`
`rArr T = 10^(@)C`