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  • In the given circuit 'a' is an arbitrary constant. The value of for which the equivalent circ

In the given circuit 'a' is an arbitrary constant. The value of \mathrm{m} for which the equivalent circuit resistance is minimum, will be \mathrm{\sqrt{\frac{x}{2}}}. The value of \mathrm{x} is ________.

Option: 1

3


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{Req= \frac{ma}{3}+\frac{\left ( a/m \right )}{2}}
           \mathrm{= \frac{ma}{3}+\frac{a}{2m}}
           \mathrm{= \frac{2m^{2}a+3a}{6m}}
           \mathrm{= \frac{ma}{3}+\frac{a}{2m}}

For Req to be minimum,
\mathrm{\frac{dReq}{dm}= 0}
\mathrm{\frac{a}{3}-\frac{a}{2m^{2}}= 0}
\mathrm{\frac{a}{3}= \frac{a}{2m^{2}}\; \Rightarrow\; m^{2}= \frac{3}{2}}
                             \mathrm{m= \sqrt{\frac{3}{2}}}

The answer is (3)
 

Posted by

Ritika Jonwal

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