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# Two rods are taken having same length and area and of the same material are joined side by side, heat is allowed to flow through them for 12 minutes. If now the rods are joined in parallel, then how much time will it take to flow the same amount of heat?

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a
24 minutes
b
3 minutes
c
12 minutes
d
6 minutes
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detailed solution

Correct option is B

in Series time of flow of heat ist1=12 minutes  amount of heat that flows in two rods when in series is  Q1=KseriesA(θ1-θ2)2lt1----(1)  here Kseries is coefficient of thermal conductivity when rods  are in series  A is area of cross section  θ1,θ2 is temperatures at their each end  l is length of rod  t1 is time of flow of heat     In series, effective coefficeint of thermal conductivity is Kseries,l+lKseries=lK+lK  Kseries= K     when rods are in parallel , effective coefficeint of thermal conductivity is   Kparallel=K1+K22   Kparallel=K+K2   Kparallel= K  when rods are taken in parallel, amount of heat that flows in time t2 isQ2=Kparallel2A(θ1-θ2)lt2----(2)  to find t2 equate eqn(1) and eqn(2)Q1=Q2  KseriesA(θ1-θ2)2lt1=Kparallel2A(θ1-θ2)lt2  here Kseries=Kparallel  on solving we get  t2=3 minutes      ---(1)

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Two rods of length ${\mathrm{d}}_{1}$ and ${\mathrm{d}}_{2}$ and coefficients of thermal conductivities ${\mathrm{K}}_{1}$ and ${\mathrm{K}}_{2}$ are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

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