This is almost certainly Ra, by Sam Hughes.
Magic is real.
Discovered in the 1970s, magic is now a bona fide field of engineering. There's magic in heavy industry and magic in your home. It's what's next after electricity.
Student mage Laura Ferno has designs on the future: her mother died trying to reach space using magic, and Laura wants to succeed where she failed. But first, she has to work out what went wrong. And who her mother really was.
And whether, indeed, she's dead at all...
There are ...gadgets... such as rings and "wearable electronics" that can be used to focus, pool, catalyze raw magic (mana?) to improve efficiency
But, though armed, she is drunk off her face.
A momentary pause to elaborate on what she's wearing. The key word here is "rings". The high-heeled, high-impracticality shoes have been touched upon already. The black leggings, black skirt and black top are inconsequential. Resting comfortably around her neck, though, is a very fine silver necklace made from thirty-seven components, each a unique three-dimensional elongated silver shape linked to the next with wire; this is much more significant. Decorating her ears are large silver earrings in equally complex shapes. Around her left wrist are four silver bangles and one golden bangle, all slightly different sizes, each custom-made by a different craftsperson, but engraved with the same complicated repeating and interlocking design, reminiscent of Korean text but illegible in any human language. These five are independent, but amplify each other. Around her right wrist are three more bangles, these ones relatively commonplace items bought "off the shelf", albeit a specialist and extremely expensive and obscure shelf. These three interlock and (in ways which may become apparent) interact with one another in useful ways. On her left index finger, left thumb and left middle finger, three smaller rings with similar designs which control the bangles on her right hand. On her left ring finger, nothing (but ah, one day). On her right index finger, no rings, but an intricate tattooed design circling the base of the finger where a ring would sit.
The story starts with her going through the city and choosing to go down a side street, where she uses her self-made gadgets to get out getting mugged.
It's sixty seconds to one and she has a long zig and then zag to take to get to the top of the hill where the bus stops are, but there is thankfully a shortcut, a narrow and steeply-stepped (but usually quite well-lit and friendly) alley which cuts off the corner of the triangle, so she takes that instead. It's well-lit because the Slouch is halfway along it and usually completely filled with people. Of course, she remembers a little too late, the Slouch got closed down a couple of weeks ago because some stupid woman took drugs and almost died on their property. It'll be back, but there are legal proceedings. In the meantime, for the moment, this is quite a dark and empty passage.
A couple of men come around the corner and start coming down the steps. "'Scuse me!" she chirps, moving to slide past them on the side. They don't move. How irritating. One of them reaches into his jacket. The other already has both of his hands free.
"Her," she hears a third man utter some yards behind her.
Then Laura's had enough time to remember her emergency phrase and form a few syllables.
"Dulaku surutai jiha, twenty you em!"
She flails her right hand at her attackers and they recoil with hot pain as large amounts of hard infrared and microwave radiation wash over them like water from a fire hose. The thermal output is invisible, but immediately felt on the face and skin. The first one she hits recoils instinctively, hands across his face, cheap plastic jacket bubbling and beginning to melt in places. He runs for it, escaping down the alley steps and into the Square. The one with the Maglite takes the thermal energy in the face and throws himself back against the wall, clutching his eyes. The third ducks with surprising speed.
And the fourth sees it coming. He shields his head with his heavy leather jacket and lurches forward in front of Laura, managing to deflect her hand upwards where it's relatively safe. Her hair begins to singe and the wall starts to scorch. But before he can get hold of her other hand (and before her hair can catch fire) Laura has managed to pronounce "Kafa'u six kay dulaku!" and a quantity of directed linear momentum has erupted out of that hand like a fist into his sternum, hurling him up and backwards into the wall and along it and down into the street beyond. Even if the buses miss him he'll break a leg or two. He won't be back.
"Get her arms!" shouts Three, but there's nobody else still in the game. He cannons into her from below and pins her right hand to the wall, pointed sideways this time. But Three's too slow to get her left hand either-- maybe he thinks she needs to say the whole spell again to carry it out a second time?
"Sedo!" she says, and another invisible piston smashes Three against the far wall of the alley. CRACK go several parts of his body, and several parts of Two's body too, who was curled up on the ground right behind him. Three drops from the wall like a ragdoll and rolls down the steps. Laura manages to find her footing and slump down against the wall. "Thono," she says, which switches off her thermal lance. It's over.
She does have a sister, Natalie, who she has coffee with in the second chapter. Natalie does study magic, but is focused on the theory, while Laura is much more practical and hands-on.
In the lab, they even have industry-grade equipment with big fat cables between them (you can almost see the "Siemens" logo on the side of it)
From the fifth chapter, "What You Don't Know":
Czarnecki wheels a piece of machinery out of a corner and kicks the power switch on at the wall. The machine is a Veblen pump. It has the dimensions of a pair of upright pianos placed back to back, but it looks more like an enormous tower PC case, with the side missing and the interior filled with small magic rings and runes and tubes instead of circuitry and disk drives. Specifically, it looks like the old kind of tower - manufactured an optimistic white, but now faded to a depressing creamy beige after a few decades of use. It's a little beaten up, and could really use replacing, but as long as it continues to serve the fairly menial purpose that it needs to serve, that will never happen. On the side of the machine are some rolls of hose with more magic rings tying off the ends. Czarnecki unwinds a few turns of hose for three of the rings and hands them out to the students. He directs the gangly student to stand at twelve o'clock on the rim of the magic ring in the floor, the shorter one at eight o'clock and Laura at four. The three of them trail long hoses over the floor ring's interior.
there was an incident during a group exercise in class, where a student didn't pay enough attention and almost caused a dangerous situation had the instructor not intervened.
The accident is actually the result of Laura wearing rings to store mana and the professor not following proper procedure by checking for foreign devices. A Dr. Neal Marek, the deputy head of department, remonstrates him for it:
"Because Dr Czarnecki wasn't following procedure."
"What?" says Czarnecki. He looks up, suddenly angry and embarrassed.
"He should have made sure that none of his students had brought dangerous foreign objects into the system. He should have paid closer attention to his students while they were casting. He should have realised that something was wrong sooner and, yes, he should have warned you up front." Marek says all of this without even turning around.
Dr. Marek does establish that Dr. Czarnecki correctly detected the dangerous situation and took the correct steps once he realized the problem:
"One of the purposes of the experiment," Marek continues, "was to-- safely-- demonstrate, ah, 'low-energy high-energy magic', and introduce some of the safety concerns associated with it. If procedure had been followed, it would have been perfectly safe. As for what Dr Czarnecki did right: while he was setting up the experiment, he verified that all the raw mana held by everybody in the room combined couldn't have crossed the threshold of danger. That's by the book. When he did realise something was wrong, he quickly determined the problem and was decisive in resolving it. And he got all three you out of Tanako's world very quickly, which is a testament to his skill."
I found it with a Google search for online novel magic engineering -recluse -recluce (annoyingly, I kept getting matches for sites with pirated copies of L.E. Modesitt, Jr.'s The Magic Engineer).