Difficulty: Easy
Correct Answer: Measurement of resistance using the ratio of two balance lengths
Explanation:
Introduction / Context:
DC potentiometers are precision instruments that compare unknown voltages to a reference, typically a standard cell. Before reading absolute voltages, a potentiometer is usually standardized so that the slide-wire scale reads in true volts. However, some measurement techniques use only ratios of balance lengths, which cancel the calibration constant. This question checks whether you know which applications do and do not require standardization.
Given Data / Assumptions:
Concept / Approach:
When measuring resistance R_x by the drop across R_x and a standard R_s in the same circuit current I, the potentiometer balances two voltages that are proportional to IR_x and IR_s. The balance lengths l_x and l_s are proportional to those voltages with the same scale constant k (volts per unit length). Hence R_x / R_s = (k l_x) / (k l_s) = l_x / l_s, independent of k; therefore, standardization is unnecessary. By contrast, direct EMF measurements and instrument calibration require the absolute scale in volts, so standardization is essential. Measuring current from V = IR with a standard resistor also needs the absolute voltage value, hence requires standardization.
Step-by-Step Solution:
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Discussion & Comments