A potentiometer is a resistor with a sliding contact. It can...

A potentiometer is a resistor with a sliding contact. It can be used to measure emfs accurately (Problem 131$)$ or to supply a variable voltage to a circuit (Problem 132 ). In the diagram with switch $S_{1}$ closed and $S_{2}$ open, there is no current through the galvanometer G (a sensitive detector of current whose operation is based on magnetic forces) for $R_{1}=20.0 \Omega$ with a standard cell $\mathscr{E}_{\mathrm{s}}$ of $2.00 \mathrm{V}$. With switch $S_{2}$ closed and $S_{1}$ open, there is no current through the galvanometer G for $R_{2}=80.0 \Omega$. (a) What is the unknown emf $\mathscr{E}_{x} ?$ (b) Explain why the potentiometer accurately measures the emf even for a source with substantial internal resistance.

A potentiometer is a resistor with a sliding contact. It can be used to measure emfs accurately (Problem 131$)$ or to supply a variable voltage to a circuit (Problem 132 ). In the diagram with switch $S_{1}$ closed and $S_{2}$ open, there is no current through the galvanometer G (a sensitive detector of current whose operation is based on magnetic forces) for $R_{1}=20.0 \Omega$ with a standard cell $\mathscr{E}_{\mathrm{s}}$ of $2.00 \mathrm{V}$. With switch $S_{2}$ closed and $S_{1}$ open, there is no current through the galvanometer G for $R_{2}=80.0 \Omega$. (a) What is the unknown emf $\mathscr{E}_{x} ?$
(b) Explain why the potentiometer accurately measures the emf even for a source with substantial internal resistance.

Key Concepts

Potentiometer

A potentiometer is an electrical device that uses a long, uniform resistor with a sliding contact. It is commonly used for accurately measuring unknown electromotive forces (emfs) by creating a variable voltage against a known reference. The instrument operates on the principle that when the voltage drop across a segment of the resistor matches the unknown emf, no current flows in the detector, indicating a balance.

Null Measurement Method

The null measurement method involves adjusting a circuit parameter until the measuring instrument, often a sensitive galvanometer, indicates zero current. The condition of zero current (null) ensures that the measured voltage is not affected by the internal resistance or loading effects, leading to a highly accurate determination of the unknown quantity.

Electromotive Force (Emf)

Electromotive force (emf) is the voltage generated by a battery or cell that drives current through a circuit. In measurement techniques like potentiometry, the unknown emf is compared against a calibrated voltage reference, allowing its precise determination by equating linearly distributed voltage drops.

Internal Resistance

Internal resistance is the inherent opposition to current flow within a power source such as a battery. This resistance can cause a voltage drop when current is drawn, which can affect measurement accuracy. However, by using a null method in potentiometric measurements, no current flows from the source during the measurement, effectively eliminating the voltage drop caused by internal resistance and ensuring an accurate readout.

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