JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Current Electricity

Five identical cells each of internal resistance

1Ω

and emf 5 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?

(A) $25Ω$
(B) $10Ω$
(C) $1Ω$ ✓ Correct
(D) $5Ω$

Answer: (C)

Solution

With five cells in series the emf is

25

V and the internal resistance is

5 Ω

, so

I_{s} = \frac{25}{5 + R}

. With the five identical cells in parallel the emf stays

5

V and the internal resistance becomes

\frac{1}{5} Ω

, so

I_{p} = \frac{5}{R + 0.2}

. Equating the currents,

\frac{25}{5 + R} = \frac{5}{R + 0.2} \Rightarrow 25 (R + 0.2) = 5 (5 + R) \Rightarrow 20 R = 20,

giving

R = 1 Ω

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option

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