Two identical square rods of metal are welded end to end as shown in fig `(1)`. `20 cal` of heat flows through it in `4min`. If the rods are welded as shown in fig.`(2)`, the same amount of heat will flow through the rods in

Options

A. `1 min`
B. `2 min`
C. `4 min`
D. `16 min`

Explanation

Figure `(1) to ` series combination
Figure `(2) to` parallel combination
Thermal resitance for each to block to be `=R`
Then
Thermal resistance for case `I R_(1)=2R`
Thermal resistance for case `II`
`R_(2)=2R`
Thermal resistance for case `II`
`R_(2)=R//2`
`I_(1)=(DeltaT)/(R_(1))` `I_(2)=(DeltaT)/(R_(2))`
`implies4I_(1)=I_(2)`
`4(Deltatheta_(1))/(Deltat_(1))=(Deltatheta_(2))/(Deltat_(2))` if `Deltatheta_(1)=theta_(2)`
then
`4Deltat_(2)=Deltat_(1)`
`Deltat_(2)=Deltat_(1)//4=(4)/(4)=1min`