1. Given data

• Number of identical cells, $n = 5$
• Emf of each cell, $E = 5\text{ V}$
• Internal resistance of each cell, $r = 1\,\Omega$
• External resistance = $R$

We need the value of $R$ for which the current drawn from:

• series combination of cells, and
• parallel combination of cells

is the same.

2. Current when cells are in series

For 5 identical cells in series:

• Equivalent emf: $E_s = 5E = 5 \times 5 = 25\text{ V}$
• Equivalent internal resistance: $r_s = 5r = 5 \times 1 = 5\,\Omega$

So current through external resistance $R$ is $I_s = \frac{E_s}{R + r_s} = \frac{25}{R+5}$

3. Current when cells are in parallel

For 5 identical cells in parallel:

• Equivalent emf remains same as one cell: $E_p = E = 5\text{ V}$
• Equivalent internal resistance: $r_p = \frac{r}{5} = \frac{1}{5}\,\Omega$

So current through external resistance $R$ is $I_p = \frac{E_p}{R + r_p} = \frac{5}{R + \frac{1}{5}}$

4. Condition for equal currents

Given: $I_s = I_p$

So, $\frac{25}{R+5} = \frac{5}{R + \frac{1}{5}}$

Cross-multiplying: $25\left(R + \frac{1}{5}\right) = 5(R+5)$

$25R + 5 = 5R + 25$

$20R = 20$

$R = 1\,\Omega$

5. Checking options

• A: $1\,\Omega$ ✅
• B: $25\,\Omega$ ❌
• C: $5\,\Omega$ ❌
• D: $10\,\Omega$ ❌

So the correct option is A.

6. Comparison with stored correct answer

Stored correct answer: A

Our derived answer: A

They match.