Answer:
The solution of the equation is [tex]R = \frac{V}{i}[/tex].
Step-by-step explanation:
The previous equations is for the Ohm's Law, which states that current ([tex]i[/tex]), measured in amperes, is directly proportional to the voltage ([tex]V[/tex]), measured in volts:
[tex]V \propto i[/tex]
The complete formula is:
[tex]I\cdot R = V[/tex] (1)
Where [tex]R[/tex] is the electric resistance, measured in ohms.
Solving for [tex]R[/tex] means that we need to clear [tex]R[/tex] within the formula, a process that will be presented step-by-step:
1) [tex]V = i\cdot R[/tex] Given
2) [tex]V\cdot i^{-1} = (i\cdot R)\cdot i^{-1}[/tex] Compatibility with multiplication.
3) [tex]V\cdot i^{-1} = R\cdot (i\cdot i^{-1})[/tex] Commutative and associative properties.
4) [tex]V\cdot i^{-1} = R\cdot 1[/tex] Existence of multiplicative inverse.
5) [tex]V\cdot i^{-1} = R[/tex] Modulative property.
6) [tex]R = \frac{V}{i}[/tex] Definition of division/Symmetric property/Result
The solution of the equation is [tex]R = \frac{V}{i}[/tex].
