when batteries of same p.d across them are connected in series ,lets say 3 of them..do they charge equally or proportionally ?

 

If they are at a different charge state, or of different capacities, then one will get fully charged first and will be overcharged while the others are still charging. It also complicates determining the fully charged threshold for the combination.

It is OK if the three cells are not lithium cells (which are particularly fussy) and are identical and new at the start and then stay in series while being discharged and recharged.

 

The batteries have internal resistance, and each of them could be different, so you can imagine that there are three resistors in series as 3mΩ, 4mΩ, 5mΩ, and then you can use the easy formula as V1=I*3mΩ, V2=I*4mΩ, V3=I*5mΩ to get 3 voltages of batteries.

 

when batteries of same p.d across them are connected in series ,lets say 3 of them..do they charge equally or proportionally ?

What does "p.d" mean? If it means what I think it means, why don't you just use the common term "voltage" instead of trying to be different?

At any rate, batteries in series will typically not charge equally. The weakest battery will spend more than the rest in overcharge which will accelerate it's demise.

When using batteries in series, the weakest battery (and there will always be one) will discharge first. It's stronger companions will drive it into reversal and this will result in the cell being damaged irrecoverably for most (all?) battery chemistries. It only takes a very small reverse current to do this.

That's why manufacturers using batteries in series tell you to change all batteries at the same time, and not to mix battery chemistries. I don't think they're as good about warning about using batteries of different mAh capacities; which is always the case because no two batteries will have identical capacity. They could be close, but never identical.