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  • The charge flowing through a resistance R varies with time as n

The charge flowing through a resistance R varies with time as \mathrm{Q=a t-b t^2}  The total heat produced in R is

Option: 1

\mathrm{\frac{a^3 R}{6 b} }


Option: 2

\mathrm{\frac{a^3 R}{3 b} }


Option: 3

\mathrm{\frac{a^3 R}{2 b} }


Option: 4

\mathrm{\frac{a^3 R}{b}}


Answers (1)

\mathrm{ Q=a t-b t^2 \Rightarrow i=d Q / d t=a-2 b t }
\mathrm{ i=0 \text { for } t=t_0=a / 2 b, }   i.e., current flows from  \mathrm{t=0 \text { to } t=t_0 \\, }
The heat produced \mathrm{=\int_0^{t_0} i^2 R d t=a^3 R / 6 b}

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Kshitij

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