Hallo David,

I would insert some low ohmic shunt resistance and meassure voltage dropping across it. Look at the following example:







If you connect probe of scope directly across shunt resistor, you can also observe fast supply current changes.

Please note, that

1. shunt resistor should not be inserted in the connection between Vcc pin and power supply decoupling capacitor, because this would worsen decoupling ability.

2. shunt resistor should be choosen so small, that voltage drop is smaller than about 200mV, otherwise Vcc would leave nominal value.

By the way, arrangement of shunt resistor and decoupling capacitor is well known as 'RC power supply filter' and is sometimes used for filtering purpose, when Vcc is very noisy...

Good luck,
Kai