Question

the formula to find the internal resistance of a battery is ( v = e - ir ), where

• ( v ) is the measured voltage when the battery is operated,
• ( e ) is the ideal voltage of the battery,
• ( i ) is the current, and
• ( r ) is the internal resistance.

which equation can be used to find ( i ), given ( v ), ( e ), and ( r )?
( \bigcirc ) a ( i = e - v + r )
( \bigcirc ) b ( i = e - v - r )
( \bigcirc ) c ( i = \frac { - v + e } { r } )
( \bigcirc ) d ( i = \frac { v - e } { r } )
( \bigcirc ) a
( \bigcirc ) b
( \bigcirc ) c
( \bigcirc ) d

Explanation:

Step1: Rearrange the formula

Given \( V = E - Ir \), we want to solve for \( I \). First, move \( Ir \) to the left - hand side and \( V \) to the right - hand side: \( Ir=E - V \).

Step2: Solve for \( I \)

Divide both sides of the equation \( Ir = E - V \) by \( r \) (assuming \( r
eq0 \)). Using the formula \( a\times b = c\Rightarrow b=\frac{c}{a}(a
eq0) \), we get \( I=\frac{E - V}{r}=\frac{-V + E}{r} \).

Answer:

C. \( I=\frac{-V + E}{r} \)