JEE Main · 2018 · 08 Apr 2018 · Offline · Current Electricity

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In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of

5Ω

, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

(A) $2.5Ω$
(B) $1Ω$
(C) $1.5Ω$ ✓ Correct
(D) $2Ω$

Answer: (C)

Solution

On open balance the full emf matches

52

cm of wire. When the cell is shunted by

5 Ω

its terminal voltage matches only

40

cm, and the ratio of balance lengths equals the ratio of terminal voltage to emf,

\frac{ε - i r}{ε} = \frac{40}{52}

with

i = \frac{ε}{5 + r}

. Substituting gives

\frac{5}{5 + r} = \frac{40}{52} = \frac{10}{13}

, so

65 = 10 (5 + r)

and

r = 1.5 Ω

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

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JEE Main · 2018 · 08 Apr 2018 · Offline · Current Electricity

Solution

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