In an electric circuit, a cell of certain emf provides a potential difference of $1.25\, {V}$ across a load resistance of $5\, \Omega .$ However, it provides a potential difference of $1\, {V}$ across a load resistance of $2\, \Omega$. The $emf$ of the cell is given by $\frac{x}{10} v$. Then the value of $x$ is ..... .
JEE MAIN 2021, Medium
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Terminal voltage $v=i R=\frac{E R}{R+r}$
$1^{s t} \rightarrow 1.25=\frac{E(5)}{5+r} . .(i)$
$2^{n d} \rightarrow 1=\frac{E(2)}{2+r}\, \cdots \text { (ii) }$
By $(i)$ and $(ii)$
$r=1 \,\Omega, E=\frac{3}{2} \,V=\frac{15}{10}\, \text { volt }$
$\Rightarrow {x}=15$
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