Question

Solve the formula for e. E/e=(R+r)/R

Answer 1

To solve the formula \( \frac{E}{e} = \frac{R + r}{R} \) for \( e \), follow these steps.

1. Start with the equation:
\[
\frac{E}{e} = \frac{R + r}{R}
\]

2. Multiply both sides by \( e \) to eliminate the fraction on the left:
\[
E = e \cdot \frac{R + r}{R}
\]

3. Next, solve for \( e \) by isolating it on one side. To do this, divide both sides by \( \frac{R + r}{R} \):
\[
e = \frac{E}{\frac{R + r}{R}}
\]

4. To simplify the right side, multiply by the reciprocal:
\[
e = E \cdot \frac{R}{R + r}
\]

Thus, the solution for \( e \) is:
\[
e = \frac{E \cdot R}{R + r}
\]