Electronic – Why can a voltmeter still measure potential difference if it has a (theoretically) infinite resistance

voltage measurement

I am a physics teacher who did engineering and hated all things electrical! Hence when my students sometimes ask me how a voltmeter can measure the potential difference between two points if there is no current passing through the voltmeter. I can only assume that it is because having an infinite resistance is impossible, but I have never had the confidence to answer this without worrying about feeding them incorrect information.

My idea as it stands is that the resistance of a voltmeter is only theoretically infinite, in which case there will be a current flowing, however small, that can be used somehow by the voltmeter of a predetermined resistance to calculate the actual potential difference.

Can somebody explain whether I am along the right lines with this and help me explain this in definite terms or at least disabuse me of my assumptions and tell me the correct idea?

Best Answer

The underlying difficulty seems to be the belief that some current must flow to measure voltage. This is false. Since you are a physics teacher, I'll explain by making analogies to other physical systems.

Say we have two sealed vessels, each filled with some fluid. We want to measure the pressure difference between them. Like voltage, relative pressure is a difference in potentials.

We could connect them with a tube which is blocked in its middle by a rubber diaphragm. Some fluid will move initially, but only until the diaphragm stretches to balance the forces of the fluids acting on it. We can then infer the pressure difference from the deflection of the diaphragm.

This meets the definition of infinite resistance in the electrical analogy, since once this system has reached equilibrium, no current flows (neglecting diffusion through the diaphragm, which can be made arbitrarily small and isn't necessary for the operation of the device).

However, it does not qualify as infinite impedance, because it has non-zero capacitance. In fact, this device is exactly Bill Beaty's favorite mental model of a capacitor:

capacitor (water analogy)

There are, in fact, devices that measure voltage that work analogously. Most electroscopes fall into this category. For example, the pith ball electroscope:

pith ball electroscope

Many of these devices are very old and require very high voltages to work. However, modern MOSFETs are essentially the same thing at a microscopic scale in that their input looks like a capacitor. Instead of deflecting a ball, the voltage modulates the conductivity of a semiconductor:

MOSFET structure

The MOSFET works by altering the conductivity of a channel between the source (S) and drain (D) as a function of the voltage between the gate (G) and the bulk (B). The gate is separated from the rest of the transistor usually by a thin layer of silicon dioxide (white in picture above), a very good insulator, and like the diaphragm device before, whatever very small leakage there is isn't relevant to the operation of the device. We can then measure the conductivity of the channel, and the current flowing in this channel can be supplied by a separate battery and not the device under test. Thus, we can measure a voltage with an extremely high (theoretically infinite) input resistance.

schematic

simulate this circuit – Schematic created using CircuitLab