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A potentiometer wire AB of length 100 cm has total resistance 10 ohm and is connected across a 10 V source. A balance (zero galvanometer deflection) is obtained at point C located 40 cm from A. The lower (test) loop consists of a 5 V cell of internal resistance 1 ohm in series with the galvanometer and an unknown resistance R. Find R.

1. 4 ohm
2. 6 ohm
3. 8 ohm
4. 10 ohm

Correct answer: 4 ohm

Solution

The 40 cm segment supplies 4 V, which must equal the drop across R driven by the 5 V cell through (R + 1 ohm); solving 4 = 5R/(R+1) gives R = 4 ohm.

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