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Question:

A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current i. It is found that when R=4Ω, the current is 1A; when R is increased to 9Ω, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.

Solution:

Here the terminal voltage ,V=E−ir.. (1)
and the current i=E/(R+r)
Now,V=E−E(R+r)r=ER/R+r=E(1+r/R)=.. (2)
According to equation (1) and (2), the graph V vs i and V vs R will be as shown in figure.
As i=E/(R+r)
so 1=E/(4+r) or E=4+r.. (3)
and 0.5=E/(9+r) or 2E=9+r (4)
using (3), 2(4+r)=9+r or r=1Ω
Thus, E=4+1=5V