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  4. In an electric circuit, a call of certain emf provides a potential difference of 1.25 V across a load resistance of 5 Ω. However, it provides a potential difference of 1 V across a load resistance of 2 Ω. The emf of the cell is given by (x/10) V. Then the value of x is.

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Q. In an electric circuit, a call 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 MainJEE Main 2021Current Electricity

Solution:

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Terminal voltage $v=i R=\frac{E R}{R+r}$
$1^{s t} \rightarrow 1.25=\frac{E(5)}{5+r} \ldots \ldots$ (i)
$2^{\text {nd }} \rightarrow 1=\frac{E(2)}{2+r} \ldots \ldots$ (ii)
By (i) and (ii)
$r=1 \Omega, E=\frac{3}{2} V=\frac{15}{10}$ volt
$\Rightarrow x=15$