Relation between electromotive force,internal resistance and terminal potential.

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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