The Ohmmeter

The ohmmeter measures the resistance of a component. Unlike the other two instruments, it does not merely “listen” to the circuit: it contains an internal battery, in series with an ammeter. The battery drives a known current through the component, the ammeter measures it, and from Ohm’s law the instrument obtains the resistance: $R = \frac{\Delta V}{i}$

Precisely because it uses its own source, the ohmmeter must only be connected to a component disconnected from the rest of the circuit and unpowered.

Never on a powered circuit

An ohmmeter must not be used on a live circuit: the external voltage adds to that of the internal battery and corrupts the reading; in the worst cases the instrument burns out. The component to be measured must always be isolated.

Summary — how the three instruments are connected

Ammeter: in series, small internal resistance ($r_A \ll R$). Voltmeter: in parallel, large internal resistance ($R_V \gg R$). Ohmmeter: only on a disconnected, unpowered component.

Example — measuring $i$ and $V$ together

A voltmeter with $R_V = 10\;\text{M}\Omega$ and an ammeter with $r_A = 0{,}1\;\Omega$ simultaneously measure the current and voltage across a resistor $R = 1\;\text{k}\Omega$ powered at $V_0 = 10\;\text{V}$. The true current without instruments would be $i_0 = V_0/R = 10\;\text{mA}$. With the ammeter in series it drops to $i = V_0/(R+r_A) \approx 9{,}999\;\text{mA}$ (error $-10^{-4}$); the voltmeter in parallel reduces the equivalent resistance from $R$ to $R \parallel R_V \approx 999{,}9\;\Omega$ (error $-10^{-4}$). Both errors amount to barely a tenth of a per mille: in practice, ideal instruments. Only for very large or very small resistances do these numbers become a problem.

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Topics: Circuiti elettrici Concepts: Legge di Ohm

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