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A potentiometer wire has length 4 m and resistance 8Ω. The resistance that must be connected in series with the wire and an accumulator of e.m.f. 2V, so as to get a potential gradient 1 mV per cm on the wire is

1. 40 Ω
2. 44 Ω
3. 48 Ω
4. 32 Ω

Correct answer: 40 Ω

Solution

The potential gradient is given as 1 mV/cm, which is equivalent to 0.01 V/cm or 1 V/m. For a 4 m wire, the total potential drop across the wire should be 4 V. The current through the wire is I = V/R = 4/8 = 0.5 A. The total resistance required in the circuit is R_total = E/I = 2/0.5 = 4 Ω. Since the wire already has 8 Ω resistance, the additional resistance needed is 40 Ω.

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