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www.GOALias.blogspot.comPhysicsFIGURE 3.18 (a) Sketch ofan electrolyte cell withpositive terminal P andnegative terminal N. Thegap between the electrodesis exaggerated for clarity. Aand B are points in theelectrolyte typically close toP and N. (b) the symbol fora cell, + referring to P and– referring to the Nelectrode. Electricalconnections to the cell aremade at P and N.3.11 CELLS, EMF, INTERNAL RESISTANCEWe have already mentioned that a simple device to maintain a steadycurrent in an electric circuit is the electrolytic cell. Basically a cell hastwo electrodes, called the positive (P) and the negative (N), as shown inFig. 3.18. They are immersed in an electrolytic solution. Dipped in thesolution, the electrodes exchange charges with the electrolyte. Thepositive electrode has a potential difference V +(V +> 0) betweenitself and the electrolyte solution immediately adjacent to it markedA in the figure. Similarly, the negative electrode develops a negativepotential – (V –) (V – ≥ 0) relative to the electrolyte adjacent to it,marked as B in the figure. When there is no current, the electrolytehas the same potential throughout, so that the potential differencebetween P and N is V +– (–V –) = V ++ V –. This difference is called theelectromotive force (emf) of the cell and is denoted by ε. Thusε = V ++V –> 0 (3.55)Note that ε is, actually, a potential difference and not a force. Thename emf, however, is used because of historical reasons, and wasgiven at a time when the phenomenon was not understood properly.To understand the significance of ε, consider a resistor Rconnected across the cell (Fig. 3.18). A current I flows across Rfrom C to D. As explained before, a steady current is maintainedbecause current flows from N to P through the electrolyte. Clearly,across the electrolyte the same current flows through the electrolytebut from N to P, whereas through R, it flows from P to N.The electrolyte through which a current flows has a finiteresistance r, called the internal resistance. Consider first thesituation when R is infinite so that I = V/R = 0, where V is thepotential difference between P and N. Now,V = Potential difference between P and A+ Potential difference between A and B+ Potential difference between B and N= ε (3.56)Thus, emf ε is the potential difference between the positive andnegative electrodes in an open circuit, i.e., when no current isflowing through the cell.If however R is finite, I is not zero. In that case the potentialdifference between P and N isV = V ++ V –– I r110= ε – I r (3.57)Note the negative sign in the expression (I r) for the potential differencebetween A and B. This is because the current I flows from B to A in theelectrolyte.In practical calculations, internal resistances of cells in the circuitmay be neglected when the current I is such that ε >> I r. The actualvalues of the internal resistances of cells vary from cell to cell. The internalresistance of dry cells, however, is much higher than the commonelectrolytic cells.