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Upon a six fold increase in the external resistance of a circuit, the voltage across the terminals of the battery has increased from 5V to 10V. The e.m.f. of the battery
Option: 1
$15 \mathrm{~V}$

Option: 2
$18 \mathrm{~V}$

Option: 3
$12.5 \mathrm{~V}$

Option: 4
$11 \mathrm{~V}$

Answers (1)

best_answer

$E-\frac{E}{R+r} \times r=5$ $...(1)$

$E-\frac{E}{6 R+r} \times r=10$ $...(2)$

$\text { From (1) } E\left(\frac{R}{R+r}\right)=5$ $...(3)$

$\text { From (2) } E\left(\frac{6 R}{6 R+r}\right)=10$ $...(4)$

$\frac{(3)}{(2)}, \frac{R}{R+r} \times \frac{6 R+r}{6 R}=\frac{5}{10}$

$3 R+3 r=6 R+r \text { and } 2 r=3 R$

Putting in (2) we get

$\mathrm{E}-\frac{\mathrm{E}}{4 \mathrm{r}+\mathrm{r}} \mathrm{r}=10 \text { or } \mathrm{E}-\frac{\mathrm{E}}{5}=10 \text { or } \frac{4 \mathrm{E}}{5}=10$

$\therefore \quad \mathrm{E}=12.5 \mathrm{~V}$

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