Parallel combination of cells

# Parallel combination:

In this combination anodes of all cell are joined at a point and cathode of all cells are joined at another point, between those combination points an external resistance is join along with key.

Consider m-cells are joined in parallel combination. the EMF and internal resistance of each cells be E and r respectively. the current drawn from battery so formed in external resistance R.

EMF of each cell = E volt
hence , Effective EMF of m-cell are joined in parallel combination  = E volt

And internal resistance of each cells = r  

let effective internal resistance of m cell are joined in parallel combination be r'
Thus,
1/r' = 1/r+1/r+1/r.........up to m term
1/r' = m/r
Hence, { r' = r/m }

Total resistance of the circuit = (R + r/m)

Current drawn from the battery
I = (Total EMF) / (Total resistance)
I = E / ( R + r/m )
I = mE / mR + r

Case(1): If r<<R then we put r≈0 in enq(1)

I = mE / mR +0
I = E/R
I = current drawn from cell

Case(2): If r>>R then we put R≈O in enq(1)

I = mE / (m0 + r)
I = m×(E/r)
I = m× current drawn from a cell