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The reason this adaptor is so tiny, is that all the electronics andrea_biffi put into the battery casing are located in the wall adapter of your battery AC adapter.You can measure the capacitance of the capacitors using what is called an LCR-meter. It not only measures capacitance (C), but also inductance (L), resistance (R).The capacitors are bypass capacitors, to filter any noise, that got coupled into the cable between the wall adapter and the dummy battery. They also compensate the inductance of that wire in case of sudden changes in the current.My guess is, that the smaller capacitor is 100nF and the larger capacitor is in the range of 1 - 10 uF. The exact values probably don't matter much. Common capacitors of this type can deviate from their labelled value by -20% to +80%(!).
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