Why are physically large resistor's used sometimes ?

[MathWizard]

On some of my Keithley 1980's bench DMM's, they use resistors that must be 2-3W rated old style carbon resistors, but most of them would hardly ever have anywhere near that much power. Like on an op-amp, tying 1 of the inputs to nothing else besides a 47k, 2W resistor to GND.

So is that just for some thermal stability from the larger mass, or even to add a bit more capacitance across a larger sized resistor ? I have 1 meter opened up and I might replace a few old carbon resistors, but I don't want to mess up the calibration tho, it's good enough as is I guess. But some of them can be replaced today for sure.

[Zero999]

It's impossible to know without seeing the circuit.

As you said, thermal stability will be a reason, since there's less self-heating.

It would make sense for high value resistors. Higher values are difficult to make with a close tolerance, so need to be larger, like connecting lots of smaller, lower values in series, but you said they're just 47k, which isn't that high.

I also think lower noise could be a reason. Noise averages out, so making something larger aught to reduce the noise.

[Kleinstein]

In some cases a physical larger form is ued because of the peak voltage. This is epsecially series resistors at the inputs. Here it is common to find  physical larger ones and also several in series.

The shape of the resistors can be tricky. High grade resistors may look like carbon at first glance.

A reduction of self heat may be a factor, but here the main way is more to use low TC resistors. A larger form factor helps a little but only a little and it would hardly make sense with carbon resistors.

Resistor noise is possibly an issue, but mainly at really high performance. One could expect the excess noise to go down with the square root of the resistor material used - so a relatively weak dependenece. Here the first step is starting with a type (e.g. wire wound) that is low noise to start with. Wire wound resistors may only be available in a rather large form factor for higher values.  Some wire wound series don't come in the small sizes, sometimes even more for higher values, though 47 K is not yet really large.

[MathWizard]

I've listened to a few lectures on noise, so do you mean that with a larger collection of atoms/etc, there are more states available to the electrons, and so like going to a higher resolution monitor, the random fluctuations get more smoothed out, /more uniform over the device, so it seems less discrete ?

[Kleinstein]

With resistors there are 2 part of the noise. The often larger part is the thermal or Johnson noise. This part is the same for all resistors, just depending on the temperature and resistance.
The other part is called current noise or excess noise. This is more like fluctuations in the resistance and of an 1/f type. One sees noise voltage only if the resistor also sees significant "DC" voltage. So it depends on the position in the circuit if the noise type is important. For the excess noise the material also makes a difference.  For the excess noise more size can help. One could conder 4 x the physical size as 4 resistors connected as 2S2P. As the noise contributions are uncorrelated these would add only as the squares and would result in 1/2 the excess noise for the resistor made from 4 equal resistors.

[David Hess]

Larger resistors in multimeters are usually for meeting voltage requirements during overload, which includes clearance and creepage.  Otherwise high voltage may bridge across a device, compromising overload resistance.

Less commonly larger resistors are used for better precision.  As the voltage across the resistor increases, it heats up causing a shift in resistance from its temperature coefficient.  A physically larger resistor has a lower thermal resistance to ambient so its temperature change will be smaller.

[TimFox]

Ohm’s Law is an approximation for the current vs. voltage on a practical component.  Physically, it is a linear approximation to the current density as a function of the E field (voltage gradient).  A longer path for a given voltage reduces the gradient which reduces the non-linearity.  In a critical analog circuit using a 50 megohm SMT resistor, I had to insist on a premium 1206 component since I could demonstrate the effect at only 10 V, compared with 0603.  Similar considerations can apply to TH components, depending on the construction (where wirewound is better than carbon, for example).

[JXstaystonight]

Physically large resistors, with higher power ratings, are used in electronic circuits for reliable power dissipation, improved thermal stability, better voltage handling, mechanical durability, and possibly introducing some capacitance.

Replacing old carbon resistors with modern equivalents should maintain calibration.