I was supposed to find the potential difference across any one cell in an arrangement consisting of n cells of EMF E connected in series in a closed circuit and internal resistance r. I proceeded by finding the current in the cell. i=nE/nr=E/r Then across any one cell potential diff. is V=E-ir=E-(E/r)r =0 This answer i.e. 0 matches with the book answer. But if we sum up the pd across all cells in this way then pd across all cells would be 0. This would violate my initial assumption while finding current that pd across the circuit is nE. So where am I going wrong? Is it a misprint in the book or am I mistaken in my fundamentals?
You are mistaken about your fundamentals. Your initial assumption was that the potential difference across the resistors was nE, not the whole circuit. You implicitly assumed the difference across the whole circuit was zero when you connected the components in a closed circuit. One of Kirchhoff's laws says the sum of the voltages in a loop in zero.