Question

# The charge (in C) flowing through a resistance R varies with time (in s) as Q=2t–8t2. The total heat produced in the resistance is (for 0≤t≤18 s)

A
R6 Joules
B
R3 Joules
C
R2 Joules
D
R Joules

Solution

## The correct option is A R6 JoulesWe know that, i=dQdt=2−16t Heat =R∫1/80(i)2.dt  Heat =R∫1/80(2−16t)2.dt Heat =R∫1/80(4+256t2−64t).dt Heat =R[4t+256t33−32t2]1/80 Heat =R⎡⎢ ⎢ ⎢⎣4(18)+256(18)33−32(18)2⎤⎥ ⎥ ⎥⎦ Heat =R[(12)+16−(12)] Heat=R6 J

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