A) \[\frac{{{a}^{3}}R}{6b}\]
B) \[\frac{{{a}^{3}}R}{3b}\]
C) \[\frac{{{a}^{3}}R}{2b}\]
D) \[\frac{{{a}^{3}}R}{b}\]
Correct Answer: A
Solution :
| [a] \[Q=at-b{{t}^{2}}\] |
| \[i=a-2bt\] {for \[i=0\Rightarrow \,t=\frac{a}{2b}\]} |
| From joule's law of heating |
| \[dH={{i}^{2}}Rdt\] |
| \[H=\int\limits_{0}^{a/2b}{{{(a-2b)}^{2}}}Rdt\] |
| \[H=\frac{{{(a-2b)}^{3}}R}{-3\times 2b}\left| _{0}^{\frac{a}{2b}} \right.=\frac{{{a}^{3}}R}{6b}\] |
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