Amenities near the Folsom charger, as with other Tesla network locations, were not an obvious match for the automaker’s upscale demographic. Tesla identified places close to chain restaurants, restrooms, Wi-Fi and motels.

Twenty-two minutes after plugging in, the charger had restored 100 miles of range in the Model S. It took another 20 minutes to add the next 50 miles because the rate of charging tapers down as the battery fills. Think of it as electrons having more difficulty squeezing into an increasingly crowded space. The smart strategy for fastest charging is to arrive at a destination with a nearly empty battery.

Another five minutes of charging brought the estimated range to 254 miles, enough to make it to the next stop, Coalinga. Tesla engineers advised holding my speed to 70 miles per hour just to make sure. No restrictions were placed on air-conditioner use, though.

The Supercharger is clever in its construction. It starts with the same 10-kilowatt charger that is onboard every Model S. To build the Supercharger, the company strings together 12 of the same units, which were designed from the beginning as building blocks.

“It’s good modular engineering,” Mr. Straubel said. “We configured all the circuitry, the power and the communications so we can just stack them up.”

Each Supercharger can serve two cars, and most locations will have three units. With solar panels planned for many locations, operating costs are expected to remain low, perhaps explaining the free recharges.

My lunch stop at Harris Ranch, a hacienda-like restaurant, added 153 miles of range before my burger even arrived. So I cleared the charging spot for another Model S, a Tesla company vehicle that had joined the trip, and returned to lunch. With way more energy than I would need to reach the next station 115 miles away, I made up time by flying along with Interstate 5’s speedy traffic.