Why battery got damaged, when we join battery wire in wrong polarity ?

Connecting a battery in reverse polarity can damage the various electronic and other parts in the car. Generally fuses and diodes are there to protect the circuits in case of such an error but if they do not stand to the reverse polarity as intended then it is quite possible that high reverse current will flow in the car electronics and other parts like alternators etc and a lot of damage would be there.
In fact when we connect a battery wrongly then instead of +12 volt DC power we are supplying -12 volt to the car circuitry and that would only cause destruction, burning, and other electrical damages. If your car has special fuses and diode protections installed then the damage would be less. In old cars generally there is a tendency of the road side mechanics to put simple electric wire in place of the fuse in the fuse box and in such cases the damage due to wrong battery connection can be well understood as that wire does not blow out and does not protect the circuit. In such situation even the battery itself gets damaged due to the high current flow through it.

It is known that generally, cars will be using lead-acid batteries which are known as secondary batteries. It may be called an accumulator also. A secondary battery is a device that converts chemical energy into electrical energy. The so produced electrical energy will be used later while we start the car.

The chemical reactions that will take place in these secondary cells are reversible. This reverse reaction will take place when the battery is connected in the reverse direction. When the current has reversed the products formed in the cell will get back to the original materials that are kept. When the battery is connected in reverse, reverse polarity will take place and the following damages will happen.

1. All electronic components may get burnt out.
2. This may damage partially or completely the charger circuit that is provided in the car.
3, The battery may be heated up and may explode also.
4. The battery may get discharged completely and may get damaged permanently.
5. The heat produced by the reverse polarity in the battery may cause hydrogen gas that may explode the casing of the battery. This will allow the acid from the battery to flow out and damage the other components of the car engine.

These days advanced versions of batteries coming in which some protection mechanism from this reverse connection that will use special diodes and fuses. In such cases the damages may not be there because of the fuses that will get blown off and the current flow will get disconnected.

Sometimes when the battery is completely discharged by doing this reverse connection some people try charging the battery. But it may not give good results and should not be used.

In case, the battery terminals are connected to wrong polarities, it would cause serious damage to the battery itself, the electrical components and even you would be hurting yourself due to the chances of serious explosion in the wake of connection of wrong terminals.
The battery terminals use 12 voltage on either side of the terminals. The positive side would draw a voltage of +12 V while the negative one would use - 12 V. If the circuit is allowed to operate, the battery will try to adjust making negative 12 V to positive one which would cause excess built up of power accompanying enormous amount of heat which would beyond tolerance for the system. Ultimately it would cause serious damage to the battery to the extent that it might explode.
Damage to the Car Battery - The electrolyte within the system of the battery will boil due to the development of excess heat. Finally the excess heat would damage the external part of the battery including the terminals and the plastic top attached to the battery.
Apart from that it would even cause irreparable damage to the alternator.