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Question
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 ?
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Solution 1
Let E and r be the EMF and internal resistance of all cells respectively and e and r' be the EMF and internal resistance of each cell respectively.
As we know,
According to the definition of the terminal potential difference,
V = E − Ir
E is the EMF and r is the total internal resistance of the circuit.
I = 0 ⇒ V = E
From the graph we can see
E = 6 V
As there are three cells we can write,
E = 3 × e ⇒ e = 2 V
And, when, V = 0
⇒ E = Ir
`r=E/T=6/1=6Omega`
As per the question the cells are connected in the series, so we can write.
`r'=r/3=2Omega`
Solution 2
Since there are three cells connected in series, Total EMF = E1 + E2 + E3
We can observe from the graph that,
E1 + E2 + E3 = 6
3E = 6 (E = E1 = E2 = E3, as they are identical cells)
hence, The EMF of each cell is 2Volt.
Now, similarly, the internal resistance is also 2 Ohm for each, because in series combination of cells not only the Emf the internal resistance also gets added up.
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