Question

A cell supplies a current of 0.6 A through a $2\Omega$ coil and a current of 0.3 A through and $8\Omega$ coil. Calculate the EMF and the internal resistance of the cell.
[4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 1 Mark
Emf: 1 Mark
Internal resistance: 1 mark

Let $r$ be the internal resistance and $ϵ$ be the EMF of the cell.
Then applying the formula $I=\frac{ϵ}{R+r}$, we get:
$0.6=\frac{ϵ}{2+r}$ ...(i)
and $0.3=\frac{ϵ}{8+r}$ ...(ii)
Dividing Eq. (i) b Eq. (ii), we get:
$\frac{0.6}{0.3}=\frac{\frac{ϵ}{2+r}}{\frac{ϵ}{8+r}}$

$or$ $2=\frac{8+r}{2+r}\Rightarrow r=4\Omega$
Putting the value of $r$ in Rq. (i), we get;
$0.6=\frac{ϵ}{2+4}$
or $ϵ=3.6V$