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Question

# Two identical rectangular rods of metal of thermal resistance R, are welded end to end as shown in figure (i) and 10 J of heat flows through the rods in 2 min. How long would it take for 30 J of heat to flow through the rods if they are welded as shown in figure (ii)

A
2 min
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B
1.5 min
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C
1 min
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D
4 min
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Solution

## The correct option is B 1.5 minThe thermal resistance of each rod is R. In case (i) the rods are in series. ∴ Rs = R + R = 2R Rate of flow of heat will be dQdt=Δ TRs;102=(100−0)2R∴R=10 In case (ii) the rods are parallel; so IRp=IR+IR⇒Rp=R2=5 Now, rate of flow of heat in this case will be dQdt=ΔTRp⇒30t=[100−05] Or t = 1.5 minute.

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