Of course! Let's solve for the voltage [tex]\( V \)[/tex] given the formula for resistance of a conductor, which is:
[tex]\[ r = \frac{V}{I} \][/tex]
Here, [tex]\( r \)[/tex] represents the resistance, [tex]\( V \)[/tex] represents the voltage, and [tex]\( I \)[/tex] represents the current.
### Steps to Solve for [tex]\( V \)[/tex]:
1. Start with the given formula for resistance:
[tex]\[ r = \frac{V}{I} \][/tex]
2. To isolate [tex]\( V \)[/tex], we need to eliminate [tex]\( I \)[/tex] from the denominator. Multiply both sides of the equation by [tex]\( I \)[/tex]:
[tex]\[ r \cdot I = \frac{V}{I} \cdot I \][/tex]
3. Simplify the right side of the equation. The [tex]\( I \)[/tex]'s cancel each other out:
[tex]\[ r \cdot I = V \][/tex]
4. Thus, the formula for voltage [tex]\( V \)[/tex] is:
[tex]\[ V = r \cdot I \][/tex]
### Example Calculation:
Let's assign some example values to resistance and current to find [tex]\( V \)[/tex]:
- Let [tex]\( r = 10 \)[/tex] ohms
- Let [tex]\( I = 2 \)[/tex] amperes
Now, plug these values into the formula we derived:
[tex]\[ V = r \cdot I \][/tex]
Substitute the values:
[tex]\[ V = 10 \, \text{ohms} \times 2 \, \text{amperes} \][/tex]
[tex]\[ V = 20 \, \text{volts} \][/tex]
So, the calculated voltage [tex]\( V \)[/tex] is [tex]\( 20 \)[/tex] volts.
