Verified Solution • 2025–26 Session moderate

QNEET-2016-Ph-1084: NEET 2016 Physics - Class 12 NEET-2016-Ph-1084 Solution: The charge flowing through a resistance R varies with time t is …

The charge flowing through a resistance R varies with time t is Q=at−bt2Q = at - bt^2 where a and b are positive constants. The total heat produced in R is a3R2b\frac{a^3R}{2b} a3Rb\frac{a^3R}{b} a3R6b\frac{a^3R}{6b} a3R3b\frac{a^3R}{3b}

Multiple Choice Options

  • A a3R2b{{{a^3}R} \over {2b}} 2 b a 3 R _
  • B a3Rb{{{a^3}R} \over {b}} b a 3 R _
  • C a3R6b{{{a^3}R} \over {6b}} 6 b a 3 R _
  • D a3R3b{{{a^3}R} \over {3b}} 3 b a 3 R _

Step-by-Step Verified Solution

Given: Charge Q = at � bt 2 _ Current i = � Q � t = a _ 2 b t { f o r i = 0 _ t = a 2 b } From joule's law of heating, heat produced dH = i 2 Rdt H = � 0 a / 2 b ( a _ 2 b t ) 2 R d t H = ( a _ 2 b t ) 2 R _ 3 _ 2 b | 0 a 2 b = a 3 R 6 b

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