Electricity is a form of energy fundamental to Muggle technology and daily life. Within the Wizarding world, it is a largely foreign concept, and its associated devices are generally incompatible with heavily magical environments. Wizards and witches primarily use magic to achieve outcomes for which Muggles depend on electrical power, such as providing light, communication, and entertainment.
The most definitive explanation for the failure of electricity in the magical world comes from Hogwarts, A History. In their fourth year, Hermione Granger explains to Harry Potter and Ron Weasley why electronic surveillance devices would not work on the Hogwarts grounds.
This principle explains the widespread use of pre-industrial technology in the Wizarding world, such as quills, parchment, and candles, even in the modern era.
Most wizards display a profound lack of understanding regarding electricity and Muggle technology in general. Arthur Weasley, despite his position in the Misuse of Muggle Artefacts Office, famously expresses a naive fascination with the concept, which he pronounces “eckeltricity,” and is deeply curious about the function of items like electrical plugs. Wizards have developed magical substitutes for nearly every electrical appliance:
A notable exception to this rule is the small, portable radio that Harry, Ron, and Hermione use to listen to the clandestine Potterwatch program during the Second Wizarding War. While the text does not explain how it functions, Hermione mentions that getting a clear signal through the various protective enchantments they used was very difficult. This suggests the primary obstacle was magical interference with the signal rather than a complete power failure of the device itself.