To find the formula for the current [tex]\( I \)[/tex] in terms of the power [tex]\( P \)[/tex] and resistance [tex]\( R \)[/tex], we can start from the given formula for electrical power:
[tex]\[ P = I^2 R \][/tex]
We need to express [tex]\( I \)[/tex] in terms of [tex]\( P \)[/tex] and [tex]\( R \)[/tex]. Follow these steps:
1. Start from the given formula:
[tex]\[ P = I^2 R \][/tex]
2. Isolate [tex]\( I^2 \)[/tex]:
To solve for [tex]\( I^2 \)[/tex], divide both sides of the equation by [tex]\( R \)[/tex]:
[tex]\[ \frac{P}{R} = I^2 \][/tex]
3. Solve for [tex]\( I \)[/tex]:
To isolate [tex]\( I \)[/tex], take the square root of both sides:
[tex]\[ I = \sqrt{\frac{P}{R}} \][/tex]
Thus, the correct formula for [tex]\( I \)[/tex] in terms of [tex]\( P \)[/tex] and [tex]\( R \)[/tex] is:
[tex]\[ I = \sqrt{\frac{P}{R}} \][/tex]
Therefore, the correct choice from the given options is:
2) [tex]\( I = \sqrt{\frac{P}{R}} \)[/tex]
