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A battery consists of a variable number n of identical cells (having internal resistance r each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct relationship between I and n?

Asked in NEET 2018 · Combination of cells

• (1) (1) horizontal straight line: I does not change with n
• (2) (2) straight line through the origin with positive slope
• (3) (3) curve rising from the origin and levelling off
• (4) (4) curve rising from the origin ever more steeply

Step-by-step solution

Why the other options are wrong

• (2) Adds the emfs but forgets that the internal resistances add too, giving I∝ n.
• (3) This is the shape of I=(nε)/(R+nr) with an external resistance R; the terminals are short-circuited, so R=0.
• (4) No single slip gives a curve that steepens; that would need I to grow faster than n, which neither the emf nor the resistance can produce.

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