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# Relation between electromotive force,internal resistance and terminal potential.

In this topic we will discuss about electromotive force,internal resistance and terminal potential,relation between them . Also we will plot the graph between them .

EMF , Internal resistance and terminal potential difference of a cell

EMF of a cell –  As we know electric current flows through a complete closed circuit ,when there is an source of external force which can bring the ions from low potential to high potential . This external for which makes the current carriers to move in a definite direction called electromotive force (EMF) . In another words we can define ‘ It is the maximum potential difference between two electrodes of the cell when no current flows through the circuits i.e. in open (off) circuit‘ .

Unit of the EMF is Volt (V) and it is generally represented by ‘ε’.

Internal resistance

It is the resistance offered by the electrodes and electrolytes of a cell to the passes of electric current through it. It is denoted by ‘r’ .

its value is generally very low its value increases when cell becomes older and older .

The value of internal resistance depends on (a)area of the electrodes immersed in the electrolytes ,(ii)nature of electrodes , (iii) distance between the electrodes and (iv)nature of electrolytes .

Terminal potential difference –  Terminal potential difference of a cell is defined as the potential difference between the two electrodes of a cell in a closed circuit . it is denoted by ‘V’ . or simply we can define when current flows through a circuit then the potential difference across the end of the resistor. In a closed circuit the terminal potential difference of a cell is always less than the EMF of the cell .

Suppose , ε is the EMF of the cell , r is its internal resistance  which is connected with an external resistance R with the help of a key ( K ) as shown in the figure ,

If the key is not closed , the circuit remain open no current flows through the circuit , the  reading of the voltmeter is equal to emf ε . [ i.e. terminal potential of the cell is equal to the emf of the cell( V= ε) ] .

When key is closed then current start flowing through the circuit,

in that case emf of the cell   ε= I(R+r) = IR +Ir = V +Ir

so we can write , V = ε -Ir ………………..eq.

from the above equation  we just come to know ;

case (1)- if circuit is open ( off) I=0   so, V = ε

case (2) – If circuit is closed (on) , then  V < ε

case (3) –  ** During the charging V > ε ;

From the above equation  V = ε -Ir

We can find  internal resistance  r = (ε -V)/I

But I=v/R  so we can write   r = ( ε-V/V) R ……eq. to find the internal resistance of the cell .

Graph between (a) ε and R (b) V and R (c) V and I; are  given below –

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