How do you solve for e in $\frac{E}{e} = \frac{R + r}{r}$ $E/e=(R+r)/r$ ?

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Answer 1 · 2017-03-16T16:05:55

$e = \frac{r E}{R + r}$ $e=(rE)/(R+r)$

Given: $\frac{E}{e} = \frac{R + r}{r}$ $" "E/e=(R+r)/r$

Using first principles:

$YOU CAN DO THIS: \to Turn everything upside down giving:$ $color(blue)("YOU CAN DO THIS:"->"Turn everything upside down giving:")$

$\frac{e}{E} = \frac{r}{R + r}$ $color(green)(e/E=r/(R+r))$

Multiply both sides by E

$\frac{e}{E} \times E = \frac{r}{R + r} \times E$ $color(green)(e/Ecolor(red)(xxE)" "=" "r/(R+r)color(red)(xxE))$

$e \times \frac{E}{E} = \frac{r E}{R + r}$ $color(green)(e xx(color(red)(E))/E" "=" "(rE)/(R+r)$

But $\frac{E}{E} = 1$ $E/E=1$ and $1 \times e = e$ $1xxe=e$

$e = \frac{r E}{R + r}$ $e=(rE)/(R+r)$

How do you solve for e in Ee=R+rrE/e=(R+r)/r?