Slide-wire potentiometer calibration: A 1.0185 V standard cell balances at 60 cm. With an unknown EMF connected, balance is at 82 cm. Compute the unknown EMF.

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:

  • Standard cell Es = 1.0185 V balances at length Ls = 60 cm.
  • Unknown EMF Ex balances at length Lx = 82 cm.
  • Wire is uniform: voltage drop is proportional to length.
  • Measurements are taken under null (no current drawn) conditions.


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:

Compute scale constant: k = Es / Ls = 1.0185 V / 60 cm ≈ 0.016975 V/cm.Apply to unknown: Ex = k * Lx = 0.016975 * 82 ≈ 1.3920 V.Round suitably: Ex ≈ 1.39 V.


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:

  • 0.75 V: would imply Lx ≈ 44 cm at this calibration.
  • 13.9 V / 7.45 V: order-of-magnitude errors; potentiometer ranges are typically a few volts.
  • 1.18 V: does not match the proportional ratio.


Common Pitfalls:

  • Mixing up centimeters with millimeters or switching numerator/denominator in the ratio.
  • Forgetting that the potentiometer must be re-standardized if the current through the slide wire changes.


Final Answer:

1.39 V

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