Three rods made of same material and having the same cross-section have been joined as shown. In the figure.Each rod is of the same length. The left and right ends are kept at `0^@C and 90^@C` respectively. The temperature of the junction of the three rods will be

Options

A. `45^(@)C`
B. `60^(@)C`
C. `30^(@)C`
D. `20^(@)C`

Answer

B

Explanation

Let temperature ofjunction is `T^(@)C`
`i_(1)+i_(2)+i_(3)=0`
`implies (Deltatheta_(1))/(R)+(Deltatheta_(2))/(R)+(Deltatheta_(3))/(R)=0`
`implies (T-0)/ ( R ) + (T-90)/( R )+(T-90)/( R )=0`
`implies +T+T-90+T-90=0`
`implies 3T=180`
`T=60^(@)C`