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The formula for the resistance of a conductor with voltage [tex]\( V \)[/tex] and current [tex]\( I \)[/tex] is [tex]\( R = \frac{V}{I} \)[/tex]. Solve for [tex]\( V \)[/tex].

Sagot :

GinnyAnsweridn
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.
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