I read a story in a science fiction anthology wherein the major scientific discovery was a perfect battery, which led to numerous advances in communications, transportation, and even social issues, etc.
I feel like it was a Poul Anderson story from the 50s or 60s, and the anthology was maybe from the 1970s.
I think you are referring to the Poul Anderson story "Snowball." It wasn't a battery, it was "capacitite" used to make supercapacitors for energy storage.
According to isfdb, it was anthologized in 1991, in "Power," edited by S. M. Stirling. Originally published in "If" in 1955.
It’s Snowball all right – and you weren’t wrong about the battery. See the following from the central character’s wife.
"The first thing you do, my boy, is make a replacement for that so-called battery in our car. I’m tired of having the clunk die in the middle of traffic".
And from the younger generation
Colquhoun’s eldest son Robert dropped over to find Arch tinkering with his rickety ’48 Chevrolet. “Dad says you’ve got a new kind of battery” - - I’d like to buy a big piece of the stuff from you - - To run my hot rod off it” said Rob from the lofty eminence of sixteen years.- - [Rob] also discovered, more or less clandestinely, that such a car would go up to 200mph on the straightaway.
That was until his father confiscated it.
Not a battery per se, but a short story about efficient energy generation was "Let There Be Light" as part of the Heinlein collection "The Man Who Sold the Moon" from the 1940s. I believe it has been anthologized a number of times since.
Let There be Light (1940) – a quick story on the research and development of the Light Panels, which can store and use solar energy in a highly efficient manner. The story opens with scientist Archibald Douglas learning the famous scientist Dr. Martin will be visiting him to speak with him about his Cold Light technology. The next day, the only person waiting for Dr. Douglas is a beautiful woman. It takes a bit, but she finally does convince him that she is indeed the famed Dr. Martin. Douglas quickly comes to respect and appreciate her intelligence and wit, and they work tirelessly to improve his Cold Light technology into a highly efficient power source. Unfortunately, this frustrates the electricity based power companies to no end, and Douglas comes up with the perfect solution.
