In an electric circuit, a cell of certain emf provides a potential… | JEE Main 2021 (22 Jul, Shift 2)

Q26JEE Main 2021 · 22 JUL · SHIFT 2Medium

Cells: EMF, Internal Resistance & Combinations

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 $\frac{x}{10}\text{ V}$ . Then the value of x is ______________.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

$V = \frac{ER}{R + r}$ , so $E = V\left(1 + \frac{r}{R}\right)$
$1.25\left(1 + \frac{r}{5}\right) = 1\left(1 + \frac{r}{2}\right) \Rightarrow 1.25 + 0.25r = 1 + 0.5r \Rightarrow r = 1\ \Omega$
$E = 1 \times (1 + 0.5) = 1.5\text{ V} = \frac{15}{10}\text{ V}$
$x = 15$

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