Two identical square rods of metal are welded end to end as shown in figure (i), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (ii), the same amount of heat will flow through the rods in

Options

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

Answer

A

Explanation

Rate of heat flow, `Q/t=(KADeltaT)/l = DeltaT/(l//KA)=(DeltaT)/R` (R=Thermal resistance)
`rArr t alpha R` `(therefore`Q and `DeltaT` "are same")`
`rArr t_(p)/t_(s)=R_(p)/R_(s) = (R//2)/(2R)= 1/4`
`t_(p)=t_(s)/4=4/4=1min`
(Series resistance, `R_(s) = R_(1)+R_(2)` and parallel resistance,
`R_(p)=((R_(1)R_(2))/(R_(1)+R_(2)))`