question_answer

You have three resistors of r ohm each and a battery of E volts. How would you connect these resistors with the battery to obtain maximum current? Draw a circuit diagram to illustrate your answer and also calculate the current drawn from the battery.

Answer:

These resistances should be connected in parallel with the battery to obtain the maximum current.

Let?s its equivalent resistance be \[R\,\Omega \].

\[\frac{1}{R}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}\]

\[\frac{1}{R}=\frac{1+1+1}{r}=\frac{3}{r}\]

\[R=\frac{r}{3}\]

By Ohm?s law,   \[V\mathrm{  }=\mathrm{  }IR\]

\[\Rightarrow \]              \[Current(I)=\frac{V}{R}=\frac{E}{r/3}\]

\[=\frac{3E}{r}\]