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CBSE Class 10 Science 2016 Term 1 Paper

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Question : 16 of 36
Marks: +1, -0
You have three resistors of R ΩR\,\Omega each and a battery of EE 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.
Solution:  
These resistances should be connected in parallel with the battery to obtain the maximum current.
Let its equivalent resistance be R ΩR\,\Omega.
∴    1R=1r+1r+1r\therefore\;\; \frac{1}{R}= \frac{1}{r}+ \frac{1}{r}+ \frac{1}{r}
  1R=1+1+1r=3r\;\frac{1}{R}= \frac{1+1+1}{r}= \frac{3}{r}
⇒    R=r3\Rightarrow\;\; R=\frac{r}{3}
By Ohm's law,
V=IRV = IR
⇒     Current (I)=VR=Er3\Rightarrow\;\; \text{ Current } (I) = \frac{V}{R} = \frac{E}{\frac{r}{3}}
=3Er= \frac{3E}{r}
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