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The ratio of cross-sectional areas of two conducting wires made up of the same material and having the same length is 1:2. What will be the ratio of heat produced per second in the wires, when the same current is flowing in them?

Asked in GUJCET 2008 · Heating and power in resistors

• (1) 1:2
• (2) 1:1
• (3) 1:4
• (4) 2:1

Step-by-step solution

Why the other options are wrong

• (1) 1:2 takes resistance as proportional to area. A thinner wire has more resistance: R ∝ 1/A, so R₁ : R₂ = 2 : 1.
• (2) 1:1 assumes that equal current means equal heat. The heat per second is I²R, and the two resistances differ.
• (3) 1:4 squares the area ratio, as if the square in I²R applied to the area. The current is the same in both wires, so only R matters: H₁ : H₂ = R₁ : R₂ = 2 : 1.

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