If I is the current in the external resistor R and r is the internal resistance

Question

If I is the current in the external resistor R and r is the internal resistance of the cell, the equation for the whole circuit is:

            E = I(R + r)          …….(i)

            For the same current in the external resistor R, the terminal voltage is given by:

            V = IR                  …….(ii) Use equations (i) and (ii) to solve for r by eliminating I and write this equation the form: y = mx + b Identify the independent variable and the dependent variable.

This must be in the form r=mx. I must also graph this to find r when r is the slope of the graph. What should be on the x-axis and what should be on the y-axis? How will I use this slope to find r?

Explanation / Answer

E = I ( R + r ) ---------(1)

V = IR -----------(2)

from equation (1),

E = IR + Ir

E = V + Ir

so, E = Ir + V (required form)

this is of the form, y = mx + b

where y = E, m = I, x = r

and b = V

dependent variable : E

independent variable : r

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