Is voltage measurement of a battery done in series?

Question

This might be a stupid question but I can't find an explanation.

Voltage measurement is done in parallel. But when we measure the voltage of a stand alone voltage source, say a battery, it looks like we are doing it in series and yet we get the correct reading.

^{simulate this circuit – Schematic created using CircuitLab}

So we connect the voltmeter like above to measure the voltage of an isolated voltage source. Although it is connected in series, we get the correct reading.

Am I missing something here?

Answer 1

This situation is a something of a paradox, yes, but you need to understand that 'series' does not mean 'not parallel', and vice versa.

• Any components which form a loop in which current is allowed to flow are in series.

• Any loops which share the same potential difference across them are in parallel.

In your example, current flows from the one battery terminal to the other through the voltmeter, which acts like a very large resistance (10M-50M, typically). Current is flowing in a loop, therefore the two components are in series with each other. The voltage across the battery terminals is equal to the voltage across the voltmeter, therefore the two components are also in parallel with each other.

Answer 2

The voltmeter has a high ohm resistor (e.g. 10 MΩ) which is placed in series with the battery. The voltmeter is actually measuring the voltage across this resistor using an ADC (analog to digital converter) and using that voltage which is then displayed.

I replaced the voltmeter in your circuit by the one in the diagram. Right-click on the image and choose View Image to see a larger version.

In this circuit, the input resistance is a little over 11 MΩ. There is a voltage divider made up of R1 through R4 which is connected to a selector switch to select one of several voltage ranges (20 mV, 2V, 20V and 200V) to be input to the ADC (which is contained inside IC1).

In this case, you would set the range switch to 20V since you are measuring a 5V battery (and the next lower range is 2V). This creates a voltage divider with 10MΩ on the top leg, and 1MΩ+110K+1.1K on the bottom. So with a 5V input, the ADC will see

$$5V\times\frac{1MΩ+110K+1.1K}{10MΩ+1MΩ+110K+1.1K} = 5V\times\frac{1.1111MΩ}{11.1111MΩ} = 0.1V$$

When you measure the voltage across the red and black terminals, you are really measuring the voltage across a resistor divider, which is also the voltage of the battery. This is then scaled for the ADC input.

Answer 3

Look again at your picture. In this simple case the meter is in parallel with the voltage source from the perspective of voltage measurement.

The meter is also in series with the voltage source from the perspective of current that wants to flow around the loop. Hopefully the internal impedance of the volt meter is very high so very little current flows.

Answer 4

It may help you to think of it a little differently as in your example you have a power source (the battery) and a load rather than, say, two resistors in parallel.

^{simulate this circuit – Schematic created using CircuitLab}

Here we can clearly see that the two voltages are in parallel. What may not be so clear is that the currents are in anti-parallel - i.e., they are forming a loop and so, as your hunch led you to believe, the current is running in series through the loop.

Another way of looking at it: on the battery the current is exiting the '+' terminal. On the load (voltmeter) the current is entering on the '+' terminal.

Answer 5

The 'voltmeter' we normally use is really a very sensitive ammeter with a large series resistance.

What the 'voltmeter' is doing is measuring the small current that flows through it (a serial measurement) and converting this current value back into a 'voltage' reading (i.e. the voltage across the terminals = voltage across the 'voltmeter').

By Ohm's law (V=IR) we know that V is directly proportional to I, so its just a matter of how big R (the constant of proportionality) is to convert one to the other.

It's much easier to measure a current directly (even very small ones) than it is to measure voltage directly.

Examples of 'voltmeters' that are really ammeters:

A moving coil multimeter: A low cost moving coil 'voltmeter' is typically a 50uA movement ( 1000 ohm coil). For a ONE VOLT reading (full scale) we need to have a total resistance of 20K. (you'll sometimes see this marked on the meter as 20K/volt) i.e 19k (external) + 1k (meter).

The range selector switch adds suitable parallel/series resistance into the basic meter circuit

A digital multimeter - requires/measures a much lower current something like 1M0 per volt and is closer to an 'ideal' voltmeter which would take no current from the circuit (infinite resistance?).

The resistance of the 'voltmeter' is only really important if the current taken from the circuit significantly interferes with the reading. In the case of a battery (very low internal resistance) this is highly unlikely.