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Electromotive force of Battery

Electromotive force (e.m.f.) is the total voltage developed by the battery or the cell across its terminals, on open circuit. The voltmeter connected across the battery will indicate the e.m.f. of the battery or cell provided that the key K is in open position, as shown in when no current is drawn form the battery or the cell. The e.m.f. developed is independent of the area and spacing of electrodes but depends solely on the materials of the two electrodes and of the electrolyte. The e.m.f. of the cell or battery remains constant regardless of load current.

Terminal potential of the battery or cell is the potential difference across its terminals when the battery is supplying current. It is always less than e.m.f. and decreases with the increase in load current. The difference of e.m.f. and terminal potential is known as internal drop which is proportional to the current supplied by the battery.

i.e.  E-V= Internal drop in the battery
and since internal drop is proportional to load current I
 E-V=I r where r is known as internal resistance of the battery or cell.

Internal Resistance: The entire resistance encountered by a current as it flows through a cell from the –ve  terminal to the +ve terminal is known as the internal resistance of the cell. Such resistance lies in the electrodes, I the contact surface between the electrodes and the electrolyte and in the electrolyte itself. As in any other conductor of electricity, the resistance of the cell depends on the materials, the x-sectional area, the length of the current pate (spacing between electrodes) and the temperature. Thus the area (size) and spacing of the electrodes affect the internal resistance of a cell. The internal resistance of the cell is assumed to remain constant irrespective o load current delivered by the cell. Since the internal resistance of the cell (r) is in series with the external circuit resistance R, therefore total resistance of the circuit across the cell = R + r

Current delivered, I = E.M.F.  = E
                                R+r       R+r

P.D. across the load circuit, V = IR = E x R

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