A) \[{{a}^{3}}R/6b\]
B) \[{{a}^{3}}R/3b\]
C) \[\frac{{{a}^{3}}R}{2b}\]
D) \[\frac{{{a}^{3}}R}{b}\]
Correct Answer: A
Solution :
[a] \[Q=at-b{{t}^{2}}\text{ }i=\frac{dQ}{dt}=a-2bt\] \[i=0\text{ for }t={{t}_{0}}=a/2b,\text{ i}\text{.e}\text{.,}\] current flow from The heat produced=\[\int\limits_{0}^{{{t}_{0}}}{{{i}^{2}}\,R\,dt.}\] Putting the value of I we get heat produced\[=\frac{{{a}^{3}}R}{6b}.\]
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