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