Difficulty: Easy
Correct Answer: 1.39 V
Explanation:
Introduction / Context:
A DC slide-wire potentiometer measures an unknown EMF by balancing it against a known potential drop along a uniform resistance wire. Once calibrated using a standard cell, the instrument provides highly accurate voltage measurements without drawing current from the unknown source at balance. This question requires applying the uniform scale proportionality.
Given Data / Assumptions:
Concept / Approach:
For a uniform potentiometer wire, V per cm is constant. Hence, Ex / Es = Lx / Ls. Solve directly for Ex using the ratio of balance lengths. This linear proportionality underpins the simplicity and precision of slide-wire potentiometers.
Step-by-Step Solution:
Verification / Alternative check:
Use direct ratio: Ex = Es * (Lx / Ls) = 1.0185 * (82 / 60) = 1.0185 * 1.3667 ≈ 1.392 V—same result. This cross-check confirms arithmetic and the uniform-wire assumption validity.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
1.39 V
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