If you want to find out how much of an electrical load the average residential solar installation can handle, check out a short video produced by HelioPower Inc., a company that installs solar and clean energy systems. The video was shot at the home of HelioPower VP of residential sales Scott Gordon. He basically walks around his house turning on appliances until he gets the utility meter on the house to spin forwards, signalling that the house is consuming power off the utility grid rather than from the 4 kW-worth of solar cells installed on Gordon's roof.
A couple points it pays to know: The video was shot at 2 PM under near-best-case conditions: a summer afternoon in California on a clear day. One might thus surmise the solar array is putting out power near its 4 kW capacity. And the U.S. Energy Information Administration says the average U.S. home consumes 10,896 kW-hr annually. That equates to about 1.25 kW of instantaneous load on average. So a 4 kW solar array installed on a 2,200-ft2 home, as profiled in the video, should send power back to the grid for a good portion of a day that is not wildly hot or bitterly cold.
Gordon manages to consume power from the grid by turning on his microwave oven and a pump motor for his pool, among other things. Knowledgeable electricity consumers will not be surprised. Microwave ovens and electric motors are big energy users.
Here is a link to the video: http://www.heliopower.com/videos/solar-overload