The Voltmeter

The voltmeter measures the potential difference between two nodes. It must therefore be inserted in parallel with the portion of circuit whose voltage is to be measured: its two terminals are attached to the two points between which $\Delta V$ is to be measured, without interrupting the main branch.

Principle — Ideal voltmeter

An ideal voltmeter has infinite internal resistance: it draws no current from the circuit, and so does not alter the voltage being measured.

Real instruments have a large but finite internal resistance $R_V$ (typically $R_V \geq 10^6\;\Omega$). Being in parallel with the branch, a little current still flows through it; to avoid disturbing the circuit its resistance must be much larger than that of the branch being measured: $\ev{R_V \gg R}$

Ammeter (A) in series with $R$; voltmeter (V) in parallel across $R$.

Insertion errors

A voltmeter with low internal resistance disturbs the circuit significantly: it becomes itself a “parallel branch” that drains current. For example, measuring with $R_V = 10\;\text{k}\Omega$ the voltage across a $100\;\text{k}\Omega$ resistor brings the equivalent resistance down to $9{,}1\;\text{k}\Omega$: the reading is much lower than the actual value before the instrument was connected. Rule of thumb: for accurate measurements you need $R_V \geq 100\,R$.

Series vs parallel

The ammeter and the voltmeter have opposite requirements: the ammeter (in series) must have small resistance, the voltmeter (in parallel) large resistance. In both cases the aim is not to alter the circuit being measured.

Links

Topics: Circuiti elettrici Concepts: Resistenze in serie e parallelo

Related exercises: Esercizio svolto — rete mista serie e parallelo · Problema — vero o falso su serie e parallelo · Problema — resistenza equivalente serie-parallelo