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Suppose I have a simple full wave bridge rectifier, with resistive load. Is capacitor ripple current a charging or discharging current? Or maybe it is an avarage/RMS of any current flowing through a capacitor?

On a picture below red is capacitor current, blue - line voltage, yellow - output voltage.

enter image description here

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The 'ripple current' is the current that flows in and out of the capacitor terminal, to power the load when the input voltage is low, and to recharge the caps when the input voltage is high. It is the red waveform you have identified above.

You measure it as peak to peak, or rms, depending on what you want to use the measurement for.

Use rms if you want to compute the heating in the capacitor ESR. Use peak if you want to make sure the bridge diode specification is adequate for the peaks.

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