potentiometer

Question

A potentiometer wire of length 10 m has a resistance of 20 Ω. If a cell of EMF 2 V is balanced at 400 cm, what is the potential gradient?

RankGuru · Accepted Answer

1. **Concept**: Potentiometer works on the principle that the potential drop across a segment of wire is directly proportional to its length ($E = k \cdot l$).
2. **Formulate Potential Gradient ($k$)**: $k = E / l$.
3. **Identify Balanced State**: The cell of 2 V is perfectly balanced by the potential drop of a 400 cm ($4$ m) segment.
4. **Calculation**:
   - $k = \frac{2 	ext{ V}}{4 	ext{ m}}$
   - $k = 0.5 	ext{ V/m}$.
5. **Note**: The gradient remains constant for the entire wire as long as the primary circuit current is steady.

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