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

Question

18764 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-27T22:33:52

$n = \frac{R I}{E - r I}$ $n = (RI)/(E-rI)$

Given:

$I = \frac{n E}{n r + R}$ $I = (nE)/(nr+R)$

Transpose and multiply both sides by $(n r + R)$ $(nr+R)$ to get:

$n E = (n r + R) I = n r I + R I$ $nE = (nr+R)I = nrI+RI$

Transpose and subtract $n r I$ $nrI$ from both sides to get:

$R I = n E - n r I = n (E - r I)$ $RI = nE - nrI = n(E-rI)$

Transpose and divide both sides by $(E - r I)$ $(E-rI)$ to get:

$n = \frac{R I}{E - r I}$ $n = (RI)/(E-rI)$

How do you solve for n in I=nEnr+R I = (nE)/(nr+R)?