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The charge flowing through a resistance varies with time t as where and are positive constants. The total heat produced in is
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Correct option is C
Given, Q=at-bt2∴I=dQdt=a-2bt At t=0,Q=0, I=a Also, I=0 at t=a/2b Total heat produced in resistance R,H=∫0a/2bI2Rdt=R∫0a/2b(a-2bt)2dt=R∫0a/2ba2+4b2t2-4abtdt=Ra2t+4b2t33-4abt220a/2b=Ra2×a2b+4b23×a38b3-4ab2×a24b2=a3Rb12+16-12=a3R6bSimilar Questions
Permissible current through a fuse wire of diameter 1 mm is 1A. What should be the radius of a fuse wire, made of same material, whose permissible current is 8A ?
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