Q. 5 3.8( 4 Votes )

The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown below. What is the emf and internal resistance of each cell?


Answer :

We know an cell has some internal resistance of its own due to which potential difference across cell is not as marked on it but a bit less, the marked voltage of the cell is called emf of the cell which is the potential difference across the cell when cell is not connected to external resistance or no current is being drawn from it.


Now here we have a series combination of three cells, let emf of each cell be E and internal resistance of each be r , suppose the combination is connected to an external resistance R , since cells are in series their emf’s will be added so net emf of the cell will be Enet = 3E


Internal resistances of the cells are also in series so net internal resistance of the combination is


rnet = 3r


The circuit diagram is as Shown



Now we know according to ohm’s law, the potential difference across a resistor is equal to product of current flowing through it and its Resistance Mathematically,


V = IR


Where, V is the potential difference across the ends of register, I is the current flowing through it and R is the resistance


Now potential difference across the net internal resistance of the battery or combination of cells is


V1 = Irnet


Where I is the current flowing through the circuit and rnet is the net internal resistance


In any resistance current flow from higher potential to lower potential so polarity of voltages of cell is as shown



If we let the net potential difference across battery be V so


V = Enet – V1


Or


V = Enet – Irnet


Now when current drawn from cell is 0A


i.e. I = 0 A


V = Enet


Or we can say when no current is drawn from cell, its voltage is equal to emf of the cell


From the graph we can see


When current in the circuit , I = 0 A


Voltage is V = 6 V


i.e. net emf of the cells is


Enet = 6 V


Or we can say


3E = 6 V


i.e. E = 6/3 V = 2 V


so emf of each cell is 2 V


now also from the graph


when voltage across combination of cell V = 0 V


current the circuit, I = 1 A


i.e. 0 V = Enet - Irnet


or Enet = Irnet


6 V = 1 A × rnet


So net internal resistance is


rnet = 6 Ω


or we can say


3r = 6 Ω


i.e. r = 6/3 = 2 Ω


so internal resistance of each cell is 2 Ω


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