Three identical rods of length 1 m each and cross section `1 cm^(2)` each are made of Aluminium, copper and steel respectively are maintained at `18^(@)C, 6^(@)C and 75^(@)C` respectively at separate ends. Find the temperature the common junction `[K_(Cu) =40 W//m-k, K_(Al)=200 W//m-k, K_("steel")=50 W//m-k]`

Explanation

`R_(Al)=(L)/(KA) =(1)/(200xx10^(-4)=(10^(4))/(200)`
`R_("steel") =(10^(4))/(50) and R_(Cu) =(10^(4))/(400)`
Let temperature of common junction =T
from Kirchoffs current laws `=i_(Al) +i_("steel") +i_(Cu)=0`

`(T-18)/(R_(Al)) +(T-75)/(R_("steel"))+(T-6)/(R_(Cu))=0`
`(T-18)xx200+(T-75) 50+(T-6)xx400=0`
`4(T-18) +(T-75) +(T-6)xx8=0`
`4T+T+8T=72+75+48=195`
`T=(195)/(13)=15^(@)C`