The requirements of charging a battery

A minimum of 13.4 V is required at the supply line cos for the reverse reaction to take place in a battery more voltage has to be applied

The supply current determines the time required for charging the battery so it can suit your availability well enough

Here a 60Ah source is required i think for charging in 1 hour

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what is the mathematical way of determining this ?

I'm not sure exactly. It is more of chemistry than mathematics buddy. The reverse reaction onsets only if the supply voltage is more than the voltage developed in the cell.

And for continuation we set some voltage gap as we are not sure about the impurities in the solution inside the battery

I will check on it and post it here buddy

Theorotically, applying a 60A charging current would charge a 60Ah battery in 1 hour. The charging rate is denoted as C or C-rate, in this case C = 60A. Charging time is given by C/charging current. If 120A charging current is applied, the battery will be recharged in 30 minutes.

No battery would be 100% efficient in absorbing charge. So a 60A current will make the battery take more than an hour to fully charge.Charging an ordinary battery within one hour is not recommended. It would increase the battery temperature very much and might cause damage or even fatal accidents. Also the possibility of overcharging is high in such cases.

As a rule lead acid batteries should be charged over ten hours. Faster charging leads to secondary reactions, heat and damage to the electrodes. This implies a source that can deliver 60 AH/10 = 6 amps and a voltage high enough to deliver this to the cell during the whole charge. Some means of current control must be available.
It is the current that charges. Voltage is irrelevant except that it has to be necessarily higher than the battery being charged at all times. As conqueror says the final voltage has to be above 13.4 V to ensure complete charging.
As lal says charging at high currents can be hazardous

Thankyou all

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what about lithium ion batteries ? would it be hazardous to charge them within an hour ?

the slower you charge these batteries, the high capacity it can hold. You can't charge them at high rate considering the safety of the battery. The charging current needs to be less then a threshold value, above which you would spoil the battery. This value keeps decreasing at intervals as you keep charging the battery. This is for Lithium-ion batteries. The same holds good for Pb-Acid batteries.

So, the inference is that you can't change/lessen the time of charging to a very great extent(completely charged in few min is not possible). There is a restriction.