Question

The current flowing through an external resistance of $2\Omega$ is $0.5A$ when it is connected to the terminals of a cell. This current reduces to $0.25A$ when the external resistance is $5\Omega$. Use Kirchhoff's laws to find e.m.f. of cell.
(Ans : $E=1.5V,r=1\Omega$)

Answer 1

In the figure $R$=external resistance ,$r$= internal resistance of the cell and $ϵ$= EMF of the cell

using Kirchhoff's law we can write the following equation $ϵ-IR-Ir=0$

now from the question we can write the following equations

$ϵ-2\times 0.5-0.5r=0\Rightarrow ϵ=\frac{2+r}{2}$...(1)

$ϵ-5\times 0.25-0.25r=0$...(2)

using eq(1) in eq(2) we get value of $r=1\Omega$

now using this in eq (1) we get value of $ϵ=\frac{3}{2}=1.5V$