A few simple questions about inductors..

I have an 85mA load (analog camera) that shares a power supply with a 4A load that is occasionally switched on. Even if the power supply is a car battery, the amp draw and voltage to the camera gets sucked away briefly when the 4A load is switched on causing the camera to flicker. I was thinking a 125mA, 10H inductor would maintain the current and voltage to the camera (or at least make the transitions smoother). Is this the right thinking or should I be looking at using a large cap instead?