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Two insulating sheets are stacked one on the other, the upper sheet having thermal resistance R₂ and its outer face held at temperature θ₂, and the lower sheet having thermal resistance R₁ and its outer face held at temperature θ₁. The temperature θ at the junction of the two sheets is given by

Asked in JEE Main 26th Feb 2nd Shift 2021 · Junction temperature

• (1) (θ₁R₁+θ₂R₂)/(R₁+R₂)
• (2) (θ₂R₂-θ₁R₁)/(R₂-R₁)
• (3) (θ₁R₂-θ₂R₁)/(R₂-R₁)
• (4) (θ₁R₂+θ₂R₁)/(R₁+R₂)

Step-by-step solution

Why the other options are wrong

• (1) comes from pairs each temperature with its own sheet's resistance. The weighting runs the other way: a sheet with the larger resistance holds the junction away from its own far face, so θ₂ must be weighted by R₁.
• (2) comes from writing (θ₂-θ)/(R₂)=(θ-θ₁)/(R₁) and then subtracting the cross terms instead of adding them. A quick test kills it: setting R₁=R₂ makes the denominator zero, whereas two equal sheets must put the junction at (θ₁+θ₂)/2.
• (3) comes from has the same minus-sign fault and fails the same test at R₁=R₂; here the numerator is also cross-paired, so it does not even reduce sensibly in any limit.

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