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.

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Solution

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

Let its equivalent resistance be $R Ω$
$∴ \frac{1}{R} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r}$
$\frac{1}{R} = \frac{1 + 1 + 1}{r} = \frac{3}{r}$
$\Rightarrow R = \frac{r}{3}$
By Ohm's law,
V =IR
$\Rightarrow C u r r e n t (1) = \frac{V}{R} = \frac{E}{\frac{r}{3}}$
$= \frac{3 E}{r}$

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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.

These resistances should be connected in parallel with the battery to obtain the maximum current. Let its equivalent resistance be R Ω ∴1R=1r+1r+1r 1R=1+1+1r=3r ⇒R=r3 By Ohm's law, V =IR ⇒Current(1)=VR=Er3 =3Er