Respuesta :
Answer:
(E) ε = 9.00 V, r = 1.01 Ω
Explanation:
As we know that power across the resistance is given as
[tex]P = i^2 R[/tex]
now we will have
[tex]P = 0.794 W[/tex]
[tex]R = 100 ohm[/tex]
now we have
[tex]0.794 = i^2(100)[/tex]
[tex]i = \frac{V}{100 + r}[/tex]
now we can use it as
[tex]0.794 = (\frac{V}{100 + r})^2(100)[/tex]
similarly now 100 ohm resistance is replaced by another resistance of 200 ohm
so we will have
[tex]P = 0.401 W[/tex]
[tex]R = 200 ohm[/tex]
now we have
[tex]0.401 = i^2(200)[/tex]
[tex]i = \frac{V}{200 + r}[/tex]
now we can use it as
[tex]0.401 = (\frac{V}{200 + r})^2(200)[/tex]
now we have
[tex]\frac{0.794}{0.401} = \frac{(200 + r)^2}{(100 + r)^2}\times \frac{100}{200}[/tex]
[tex]1.98 = (\frac{200 + r}{100 + r})^2 \times 0.5[/tex]
[tex]1.99 = \frac{200 + r}{100 + r}[/tex]
[tex]199 + 1.99 r = 200 + r[/tex]
[tex]r = 1.01 ohm[/tex]
now to find voltage of cell we will have
[tex]V = 9 Volts[/tex]
