JEE Physics/ Lakshmikanta Satapathy/ Direct current theory part 5/ Theory of EMF Terminal Potential Difference and Internal Resistance of a cell with complete explanation of the related concepts

1. Physics Helpline
L K Satapathy
Direct Current Theory - 5
E M F
Terminal Potential Difference
Internal Resistance
r
R
E K
V
CBA
I

2. Physics Helpline
L K Satapathy
Cells in Parallel
Direct Current Theory - 5
EMF (E) of a Cell :
It is the potential difference between the two poles of a
cell in an open circuit (when no current is drawn from
the cell). It is denoted by E .
Terminal Potential Difference (V) of a Cell :
It is the potential difference between the two poles of a
cell in a closed circuit (when current is drawn from the
cell). It is denoted by V.
Internal Resistance (r) of a Cell :
The resistance offered by the electrolyte of the cell
when electric current flows through it is called
internal resistance of the cell. It is denoted by r.

3. Physics Helpline
L K Satapathy
Cells in Parallel
Direct Current Theory - 5
r
R
E K
V
CBA
I
Consider a cell of emf E and internal resistance r connected
between points A and C in a circuit containing an external
resistance R.
When the key is closed (2nd fig) , a current I flows from left
to right through R and from right to left through r and also
through the cell. Hence r is shown outside the cell without
any loss of accuracy.
r
R
E K
V
CBA
A voltmeter V is connected across A and C , which
reads the potential difference across the cell.
 Potential Difference across the cell = ( )A CV V
Understanding the relations between E , V , r , R and I :

4. Physics Helpline
L K Satapathy
Cells in Parallel
Direct Current Theory - 5
When the key is open , current in the circuit = 0
 Potential Difference across the cell = E
, ( ) ( ) . . . (1)A C A B B CNow V V V V V V     r
R
E K
V
CBA
When I = 0 , potential drop across r = 0
( ) 0B CV V  
(1) ( ) . . . (2)A C A BV V V V E     

5. Physics Helpline
L K Satapathy
Cells in Parallel
Direct Current Theory - 5
When the key is closed , current in the circuit = I
r
R
E K
V
CBA
I
 Potential Difference across the cell = V
A is connected to the +ve and B to the –ve of the cell
( ) . . . (3)A BV V E   
Current through r is from C to B ( ) . . . (4)B CV V I r   
Current through R is from A to C ( ) . . . (5)C AV V I R   
(1) ( ) ( )A C A B B CV V V V V V E I r        
. . . (6)V E I r  Terminal Potential Difference

6. Physics Helpline
L K Satapathy
Cells in Parallel
Direct Current Theory - 5
r
R
E K
V
CBA
I
( ) ( ) ( ) 0 . . . (7)A B B C C AV V V V V V     
In the closed loop ABCA , we have
Putting the values from (3) , (4) and (5) , we get
0 ( ) . . . (8)E I r I R E I R r     
Again Potential Difference across external resistance R = IR
, (8) . . . (9)Now I R E I r V   
 Terminal Potential Difference = Potential drop across external resistance

7. Physics Helpline
L K Satapathy
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