A cell has an open circuit voltage V1 and a closed circuit voltage V2 when a current is flowing through it…

JAMB 1980

A cell has an open circuit voltage V1 and a closed circuit voltage V2 when a current is flowing through it. Therefore, the internal resistance of the cell is

A. V2/I

B. V1/I

C. (V1+V2)/I

D. (V1−V2)/I

E. (V2−V1)/I

Correct Answer: Option D

Explanation

From the relationship between EMF, Potential difference and the lost voltage we have that

E = V+v

Where E is the open circuit voltage when it is not driving any current to the external circuit

V is the closed circuit voltage the cell is now supplying current to the external circuit 

v is the lost voltage

Relating this to the questions, you have 

V1 = V2 + v

v = Ir

So, we have;

V1 = V2 + Ir

V1 – V2 = Ir

r = (V1 – V2)/I

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