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use one probe to see the voltage across the capacitor and the other probe use it to see the voltage across the resistor. The latter is directly proportional to the current. Think over about the ground terminals of the probes. They must be connected to the same node, so put the resistor adjascent to the capacitor and connect the ground of the probes to the common terminal between the resistor and the capacitor.
As far I know, you still can add a series 1Ohm resistor to each branch and see the voltage across it. Since we multiply by 1, thus the voltage will be the same exactly as the current without any differences.