I'm no electrical expert but is it something to do with Ohm's Law?
Ohm's law states that the electrical current (I) flowing in a circuit is proportional to the voltage (V) and inversely proportional to the resistance (R) i.e. I = V/R.
So, when you turn the lights on, you increase the current draw, which means the voltage also increases in proportion.
Happy to be corrected if I'm wrong!
