When connecting a battery which cable first

This question is a bit vague and not obviously entirely confined to physics. In order to make it a physics question, I'll focus on which order is better if the main concern is what happens to the circuit if we accidentally drop one of the cable's connectors.

Suppose we connect the black cable first, i.e. the one that goes on the "minus" terminal of the battery. Suppose also that the minus terminal is connected to the car chassis. Now suppose we connect the red cable to one of the batteries, and then accidentally drop the other end of the cable on somewhere on the car chassis. See the diagram.

Now we've shorted the battery, so lots of current will flow. There will probably be sparks etc. and if you leave the connection for too long (possible a very short amount of time) the battery will probably get hot and do I don't know what (i.e. catch fire/explode).

If you drop one of the connectors, it's easy for it to touch the chassis of the car because the chassis is big. On the other hand, dropping a connector onto the positive terminal of the battery is much more unlikely.

Therefore, if our main concern is what happens if we accidentally drop the cable, it's better to connect the red one first.

Jump-Starting Your Car: Complete Instructions Using Jumper Cables

Your car won’t start. What now? It might seem like your battery is dead, but if the lights and electrical systems are still running, your battery might just need a jump start. Follow these steps to give your battery a boost and get back on the road.

How to Jump Start Your Car Battery

Learn the simple steps to jump starting your vehicle battery.

STEP 1: Find Jumper Cables (Jump Leads)

Read and follow the Safety and Handling Information on this website and with the jumper cables. You'll need a set of jumper cables and another vehicle with a charged battery. You can find cables in auto parts stores, at gas stations or just about anywhere you buy car parts.

STEP 2: Park the car that needs to be jump-started next to a car with a good battery.

Park the car with the good battery next to the car with the dead battery. Pull the car close enough so that the cables will easily reach from the battery of one car to the battery of the other. Shut off both engines and prop open the hoods or trunks, depending on where the batteries are located within the vehicles.

STEP 3: Find the Red (Positive) and Black (Negative) Battery Terminals

Find the batteries and their terminals. Each battery has two metal terminals. One is marked positive (+), the other negative (-). There are also positive and negative cables in the jumper cable set. The red one is positive (+), the black one is negative (-). Never connect the red cable to the negative battery terminal or a vehicle with a dead battery.

STEP 4: Dead Battery: Identify a metal ground

Identify a metal ground within the vehicle with the dead battery. You can use the metal frame of the vehicle.

STEP 5: Dead Battery: Attach the Positive Jumper Cable Lead to a Positive Terminal

Connect a positive cable clamp to the positive (+) terminal of the dead battery.

STEP 6: Good Battery: Attach the other Positive Jumper Cable Lead to a Positive Terminal

Connect the other positive cable clamp to the positive (+) terminal of the charged battery.

STEP 7: Good Battery: Connect the Negative Jumper Cable Lead to a Negative Terminal

Connect a negative cable clamp to the negative (-) terminal of the charged battery.

STEP 8: Dead battery: Attach the other Negative Jumper Cable Lead to a Metal Ground

Connect the other negative clamp to the metal ground of the vehicle with the dead battery. You can use the engine block or another metal surface of the vehicle away from the battery. This is the last connection you need to make.

STEP 9: Dead Battery Vehicle: Start the Car

Start the car with the charged battery. Wait one or two minutes and try to start the car with the dead battery.

If the car starts:

Remove the black negative clamp from the ground of the vehicle needing the jump.

Remove the black negative clamp from the assisting vehicle.

Remove the red positive clamp from the assisting car.

Remove the red positive clamp from the formerly stalled vehicle.

If the car doesn’t start:

Wait a few moments and repeat Step 9.

We recommend fully charging your battery at the first opportunity after its being jump-started.

Which battery cable should you connect first?

By the same token, always reconnect the positive cable before connecting the negative cable. While you're servicing the battery, be sure to keep the terminals as well as the battery top between the terminals clean and debris-free.

Why do you connect positive first?

Connect positive first, negative having less potential won't arc. The higher the voltage, the greater the chance of arcing and fusion. On a car if negative first and you are touching any metal part of car, when attaching positive there is possibility of arcing through you. Your body becomes part of the circuit.