The charge flowing through a resistance R varies with time t as Q = a t - b t 2 where a and b are positive constants. The total heat produced in R is:

Step-by-step solution

given Q = a t - b t 2 i = d q d t = a - 2 b t i = 0 at t = a 2b ∴ d H = i 2 R d t = a - 2 b t 2 R   d t H = ∫ 0 a 2b a - 2 b t 2   R   d t = a - 2 b t 3 R 3 - 2 b 0 a 2b = 1 -6 b a - 2 b a 2b 3 - a 3 R = - 1 6 b 0 3 - a 3 R H = a 3 R 6 b