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7.4 EMF and r

The definition and the S.I. unit of Electromotive force (e.m.f), E

E.m.f is the potential across a cell or source of electricity when it is on ‘ open circuit ‘ and supplying no current.

The S.I. unit of e.m.f is Volt (V).

The symbol of e.m.f is E


When the cell or source of electricity in a closed circuit (current is flowing) ,the potential across the cell drops in is call the potential difference across the cell , V


V < E

Internal resistance , r

The reason why the potential difference across a cell drops when it is supplying current is that cell itself has a resistance.

The internal resistance ,r is the resistance within a cell due to its electrolyte and electrodes or source of electricity.

The electric current delivered to a circuit by a cell or battery also flows through the battery itself. Conduction inside a cell is by means of the movement of charged atoms or groups of atoms called ions in the electrolyte. There is some resistance to the flow of these ions which give a cell an internal resistance.

The S.I. unit of r is Ohm (W)

Cells in batteries

When cell is joined together to form a battery , two factors are affected by the way the cells are connected. These are the e.m.f of the battery and internal resistance of the battery. The figure following shows three typical arrangements of cells that are used.


The relationship between E,V,I,r and R



Example 1

The figure shows a circuit.


When the switch S is opened ,the reading of the voltmeter is 1.5 V. When the switch S is closed the reading of the voltmeter and ammeter are 1.35 V and 0.3 A respectively.


(a) the e.m.f. of the cell

(b) the internal resistance of the cell

(c) the resistance R


Example 2


Base on the information in the figure above,


(a) the resistance f resistor R

(b) the internal resistance ,r of the cell


Example 2

An accumulator produce a current 4 A when it is connected to a resistor 2W. When the same accumulator is connected to a resistor 3W the current is produced is 3A. Determine the e.m.f and the internal resistance of the accumulator.


Determination of E and r by using the graph method

(1) Graph V against I


From the formula E = V + Ir

E = y-axis

r = gradient

(2) Graph R against clip_image016


From the formula E = IR + Ir

E = Gradient

r = Pintasan

Experiment to determine the e.m.f. and internal resistance a dry cell.


When the switch is opened , the reading of the ammeter and voltmeter is recorded .

Later, the switch is closed and the reading of the ammeter=I and voltmeter=V is recorded.

The experiment is repeated 5 times by adjusting the rheostat.

A graph V against I is plotted.


From the graph e.m.f is the intercept on the V-axis

and r is the gradient of the graph.


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