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  • The charge flowing in a conductor varies with time as, <img alt="\mathrm{q=a t-\frac{b t^2}{2}+\frac{c t^3}{6}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bq%3Da%20t-%5Cfrac%7

The charge flowing in a conductor varies with time as, \mathrm{q=a t-\frac{b t^2}{2}+\frac{c t^3}{6}}. The minimum current in the conductor -
 

Option: 1

\mathrm{a+\frac{b^2}{2 c}}
 


Option: 2

\mathrm{a-\frac{b^2}{2 c}}
 


Option: 3

\mathrm{a-\frac{b}{2 c}}
 


Option: 4

\mathrm{a-\frac{2 b^2}{c}}


Answers (1)

best_answer

Use,\mathrm{i=\frac{d q}{d t} =\frac{d}{d t}\left(a t-\frac{b t^2}{2}+\frac{c t^3}{6}\right) }

\mathrm{i =a-b t+\frac{c t^2}{2}}                _______(1)

\mathrm{ \&\quad \frac{d i}{d t} =-b+c t}

For minimum value of current \mathrm{\frac{d i}{d t}=0}

                                           \mathrm{ 0=-b+c t }

                                            \mathrm{ t=b / c }
                                         
put in equation - 1

\mathrm{ i_{\text {min }} =a-b\left(\frac{b}{c}\right)+\frac{c}{2}\left(\frac{b}{c}\right)^2 }

\mathrm{ =a-\frac{b^2}{c}+\frac{c b^2}{2 c} }

\mathrm{ =a-\frac{b^2}{2 c} }
Hence option 2 is correct.


 

Posted by

Divya Prakash Singh

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