Get an oscilloscope and your problem will be solved. You will see a visual representation of the signal. DC is like an offset for the AC component. If the DC level is 10 volts, the average AC level is shifted 10 volts from where it would be if the DC level was 0. The scope will let you see this, and it will become intuitive for you.Here's another thing to visualize that might help you. Picture a swimming pool, only half full. So the surface is 3 feet down from the edge. Throw a rock in and ripples ride on the surface. Now pour in some water to fill the pool. It is now 3 feet higher. Throw a rock in the pool and the same ripples appear. They're the same height (amplitide) and the same rate (frequency). The only thing that's changed is the height of the surface of the pool, it's now 3 feet higher. That's the way an AC component rides on a DC component of a signal.