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CRO - do you mean cathode ray oscilloscope? That's an old term!
"Differential" - Do you mean A-B voltage measurement? Some oscilloscopes and probes provide differential inputs, but a voltage measurement doesn't directly tell you the current.
Or do you mean derivative math calculation? Some oscilloscopes provide that capability. It could estimate the current by calculating I = C*dv/dt.
To directly measure current, you can use a current probe.
Another option: maybe you can put a small-value resistor in series with the capacitor, measure the voltage across the resistor, and then calculate I = V/R.
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