Why would lights glow brighter or dimmer when running a large appliance?

Answer the lights would grow dimmer if the large appliance draws so much current that the resistance of the main electrical service conductors to that current causes a service voltage drop. Less voltage means less light one reason the lights might grow brighter when the large appliance comes on is if the rest of the household electric load (other than the large appliance)is mostly connected to just one of the service conductors, with the large appliance on the other service conductor and the service neutral is marginal or undersized. The neutral carries the unbalanced current of the two service conductors so, without the large appliance on line, the neutral is carrying a large current and the resistance of the undersized neutral to that large current is causing a voltage drop all the time, so lights are dim all the time.

When the large appliance comes on line, the unbalance is reduced, the neutral carries less current, the voltage drop reduces and the lights brighten.

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