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