The camera increases the sensitivity of the sensor by adding more electricity before it shoots. Back in the film days you did this by swapping in ISO 400 instead of your usual ISO 100.
Sorry but not correct... at least not in the way you've stated it. The sensitivity of the sensors (the photodiodes) is independent of the ISO setting. The exposure is adjusted based on the ISO setting after the image sensor has been exposed. "Adding more electricity" is not a proper technical term but I suppose you could think of an amplifier that way.
Each photodiode in a CMOS sensor does have an amplifier to boost the signal as it's being read out but again this is after the sensor has been exposed and I'm not sure this is the amplification related to the ISO setting. This is not my field of engineering and I haven't come across any definitive information about how and where in the readout process the ISO gain is implemented. There may not be any one answer as there are a number of different implementations of CMOS and CCD image sensors.