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.

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:

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