Question:

In a potentiometer experiment, cells of e.m.f. $ E_1 $ and $ E_2 $ are connected in series ($ E_1>E_2 $). The balancing length is 64 cm. If the polarity of $ E_2 $ is reversed, the balancing length becomes 32 cm. The ratio $ \dfrac{E_1}{E_2} $ is

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In potentiometer problems, balancing length ratios directly give emf ratios.

Updated On: Jan 26, 2026

$ 1 : 2 $
$ 2 : 1 $
$ 1 : 3 $
$ 3 : 1 $

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The Correct Option is D

Solution and Explanation

Step 1: Use potentiometer principle.
Balancing length is directly proportional to the net e.m.f.
Step 2: Write equations for both cases.
When cells are connected in series aiding: \[ E_1 + E_2 \propto 64 \] When polarity of $ E_2 $ is reversed: \[ E_1 - E_2 \propto 32 \]
Step 3: Convert proportionality into equations.
\[ \frac{E_1 + E_2}{E_1 - E_2} = \frac{64}{32} = 2 \]
Step 4: Solve the equation.
\[ E_1 + E_2 = 2E_1 - 2E_2 \Rightarrow E_1 = 3E_2 \]
Step 5: Conclusion.
The ratio $ \dfrac{E_1}{E_2} = 3 : 1 $.

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