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Asked in NEET-I 2016 · Heating and power in resistors
Current I = (dQ)/(dt) = a - 2bt.
Current flows until I = 0, at t₀ = a/(2b).
H = ∫₀^t₀ I²R dt = R∫₀^a/2b(a-2bt)² dt.
Put u = a - 2bt, dt = -(du)/(2b): H = R/(2b)∫₀^au² du = R/(2b)·(a³)/3.
H = (a³R)/(6b).
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