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Question

The temperature θ at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as bottom and top temperatures θ1 and θ2 (as shown in figure) is given by :



A
θ1R2+θ2R1R1+R2
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B
θ1R2θ2R1R2+R1
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C
θ1R2θ1R1R2R1
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D
θ1R1+θ2R2R1+R2
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Solution

The correct option is A θ1R2+θ2R1R1+R2
Temperature at the junction is θ.

Since the two sheets are in series combination , so the thermal current flowing through them is same .

T2TR2=TT1R1

θ2θR2=θθ1R1

R1(θ2θ)=R2(θθ1)

R1θ2R1θ=R2θR2θ1

R1θ+R2θ=R1θ2+R2θ1

θ=R1θ2+R2θ1R1+R2

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