Capacitors store charge, in your set up, it gives the necessary power output to the whole system when it is needed, it stops fluctuations in voltage drop, acts like a second temporary battery on stand by. The bigger the cap the more storage capacity. U can also parallel caps up as well in order to have a bigger storage capacity.
Yes, adding a cap or caps will solve the problem of dimming lights and it will be the cheapest and best solution.
Yes, adding a cap or caps will solve the problem of dimming lights and it will be the cheapest and best solution.