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Five identical cells

Question:

Five identical cells each of internal resistance $1 \Omega$ and emf $5 \mathrm{~V}$ are connected in series and in parallel with an external resistance ' $R$ '. For what value of ' $R$ ', current in series and parallel combination will remain the same ?

  1. $1 \Omega$

  2. $25 \Omega$

  3. $5 \Omega$

  4. $10 \Omega$


Correct Option: 1

Solution:

$\mathrm{i}_{1}=\frac{25}{5+\mathrm{R}}$

$\mathrm{i}_{2}=\frac{5}{\mathrm{R}+\frac{1}{5}}$

$\mathrm{i}_{1}=\mathrm{i}_{2} \Rightarrow 5\left(\mathrm{R}+\frac{1}{5}\right)=5+\mathrm{R}$

$4 R=4$

$\mathrm{R}=1 \Omega$

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