You cannot "underpower" an amp. An amp has an operating range in voltage that it will power at, if you drop below that voltage, then it will turn off , go into protect, or just sound like trash. An amp never has to "work" to pull power; that is a function of electrons. Electricity takes the least resistance, so if your blower fan, nav lights, and other items are on, your amp may not get the voltage it needs, and may be turning off. It has a power rail that is around 12V when the alt is off. Transistors then take that 12V and step it up/down as required to boost the signal according to the input it is receiving from the HU. All that happens when there is less voltage is the amp cannot put out at max power; more available power means the amplifier can output more, less power means it puts out less. Most amps measure output at 14.4 for RmS, and will operate from 11V-16V fine. You should audibly notice a decrease in output if you drop below 11V. A capacitor is a band-aid. The proper way to remedy a weak electrical system is to get an alternator capable of powering everything sufficiently. When a capacitor drains, it has to be recharged....this pulls power from the system, they are very non-resistive, and if the underpowering statement were true, the amp would definately be underpowered at the point immediately following capacitor drain.
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