A) \[{{e}^{-kT}}\]
B) \[{{T}^{2}}-\frac{I}{k}\]
C) \[I-\frac{k{{T}^{2}}}{2}\]
D) \[I-\frac{k{{\left( T-t \right)}^{\left. 2 \right|}}}{2}\]
Correct Answer: C
Solution :
\[\int\limits_{I}^{V(T)}{dV(t)=\int\limits_{t=0}^{T}{-k(T-t)dt}}\] \[\Rightarrow \,\,V(T)-I=k\left[ \frac{{{(T-t)}^{2}}}{2} \right]_{0}^{T}\] \[\Rightarrow \,\,\,V(T)-I=-k\left[ \frac{{{T}^{2}}}{2} \right]\] \[\Rightarrow \,\,\,V(T)=I-\frac{k{{T}^{2}}}{2}\]You need to login to perform this action.
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