How to smooth changes in *current* in a current meter?
A D'Arsonval mechanical meter movement already employs damping. If well-designed, the needle will come to rest with no overshoot. Settling time is in the 0.2 second ballpark.

It is difficult to speed response without reducing sensitivity, but slowing response to be over-damped is possible with a parallel capacitor. Over-damping should be possible with a series inductor too, but this would be very large and bulky.

For your case, 9V into a 50 ohm load would generate a current of 0.18A. If your meter has switched-scales, you'd perhaps use the next highest scale. If you have a raw meter movement, you'd use a shunt resistor in parallel with the meter movement whose value brings 0.18A to full-scale swing. An over-damping capacitor would be parallel with all:







simulate this circuit &ndash; Schematic created using CircuitLab
This example takes a 50 uA meter movement whose internal winding resistance is 3k, adds a 0.833333 ohm shunt to make a current meter that goes full-scale at 0.18 A. A damping capacitor in parallel with the shunt would have to be an enormous 120,000 uF to achieve a 0.1 second time constant. This would likely have to be a super-capacitor needing a very low voltage rating (since the meter's burden voltage is a fraction of a volt).