need to ensure the signal frequency is lower than that needed to fully charge the capacitor
measure the resistance of a 100 Ohm resistor with a multimeter
set the signal generator for sine wave at 2Vpp, 1kHz connect to scope, turn on then configure scope to average to read the “open” voltage, then return back to normal mode
connect signal generator to each end of the resistor and connect scope probes across the resistor - set scope to average to and measure the “load” voltage which will have reduced
signal generator impedance = load resistance of the resistor itself x (open voltage/load voltage - 1) and this is usually around 50 Ohms
time constant of a capacitor = combined resistance (resistance of signal generator output impedance - usually 50 Ohm + resistance of the resistor) x capacitance and the capacitor needs 5 x time constant to fully charge (99.3%), at 1 time constant it will achieve 63.3% charge
hence to ascertain what frequency to use as a starting point, use the estimated capacitance in Farads in the above equation
ascertain time to full charge and discharge by doubling the time to fully charge (ie. this makes it 10 x time constant)
take the inverse of this total time to find the maximum frequency that can be used to allow full charge and discharge cycles and this may be around 5Hz
now place the resistor in series with the capacitor and set the signal generator o square wave at this new lower frequency and 10Vpp
connect the signal generator to each end of this circuit, the probe ground to it's ground, and the probe +ve to the other side of the capacitor
you will probably need to manually adjust scale and trigger position of the scope - eg. 2V and 20msec per division, centre signal, set scope to average and adjust cursors to measure the full charge voltage which should be your input voltage, then move the cursors to measure the time to get from 0V to 63.3% of the peak voltage and this will give you the true time constant and you can feed this back into the above equation to determine the actual capacitance
you can see the actual current changes by adding a shunt resistor after the capacitor (on the ground side) and a 2nd probe connected across the shunt resistor - this may need use of high resolution mode to clean up the ch2 signal
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