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5 same cells (5V, 1Ω) connected in series and then in parallel with an external resistance R respectively if current in both circuits is equal then find the value of R.

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5 same cells (5V, 1Ω) connected in series and then in parallel with an external resistance R respectively if current in both circuits is equal then find the value of R.

(a) 4 Ω

(b) 3 Ω

(c) 2 Ω

(d) 1 Ω

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Correct answer: (d) 1 Ω

Explanation:

i1 = \(\frac{5 \in}{R+5r}i_2\)

= \(\frac{\in}{R+ \frac{r}{5}}\)

ir = iz

\(\frac{5c}{R+5r}\) = \(\frac{\in}{R + \frac{r}{5}}\)

⟹ R = r = 1 Ω

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