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  • The charge flowing through a resistance R varies with time t as Q = at - bt2, where a and b are positive constants. The total heat produced in R is:<stro

The charge flowing through a resistance R varies with time t as Q = at - bt2, where a and b are positive constants. The total heat produced in R is:

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

Q=at- bt^2\\ I=dQ/dt=a-2bt
I=0 \ for \ t=t_0=\frac{a}{2b}   i.e, current flows from t=0→t=t0
the heat produced is        \int_{0}^{t_0} i^2Rdt = \frac{a^3R}{6b}   

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chirag

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