Watch Video Demonstration here:

http://www.youtube.com/watch?v=hiWwXp95doY

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  This is a point where the screen went to a darker scene in the Clifford movie.  Note that the red and white lines showing battery voltage went up a little bit.  This is because when current to the inverter and TV goes down, the power lost or also known as the "voltage droop" or "IR drop"  in the wires connecting the battery to the inverter decreases.  And likewise, when the current to the inverter and TV goes back up, there is more of a power loss or voltage droop in the battery wiring. 

THUS we see the importance of using VERY thick wire in this situation with very robust connectors that have lots of current carrying capacity.  In this case 14 AWG size wire was used.  It's best to use the same size wire that is on your car battery, about 4 AWG.  (Yes wire size goes smaller as the actual wire cross sectional diameter gets bigger- not intuitively obvious is it??)