To find the correct equation that relates amperes, watts, and volts, we need to understand the fundamental relationship between these electrical quantities.
1. Watts (W): This is a measure of electrical power.
2. Volts (V): This is a measure of electrical potential.
3. Amperes (I): This is a measure of electrical current.
The relationship between these quantities is governed by the formula for electrical power, which is given by:
[tex]\[ P = V \times I \][/tex]
Where:
- [tex]\( P \)[/tex] is the power in watts (W),
- [tex]\( V \)[/tex] is the voltage in volts (V),
- [tex]\( I \)[/tex] is the current in amperes (A).
To express the current [tex]\( I \)[/tex] in terms of power [tex]\( P \)[/tex] (or [tex]\( W \)[/tex] for watts) and voltage [tex]\( V \)[/tex], we rearrange the above equation:
[tex]\[ I = \frac{P}{V} \][/tex]
Since [tex]\( P \)[/tex] (power) and [tex]\( W \)[/tex] are interchangeable terms in this context (both representing power in watts), the equation can also be written as:
[tex]\[ I = \frac{W}{V} \][/tex]
Now, let's check each of the provided choices to determine the correct equation:
1. [tex]\( I = \frac{W}{V} \)[/tex]
- This equation matches the rearranged formula.
2. [tex]\( I = V \times W \)[/tex]
- This suggests current is the product of volts and watts, which is incorrect as per the power formula.
3. [tex]\( I = \frac{V}{W} \)[/tex]
- This suggests current is voltage divided by watts, which is incorrect based on the formula [tex]\( P = V \times I \)[/tex].
4. [tex]\( I = W \times R \)[/tex]
- This equation introduces resistance (R), which is not part of the basic relationship we derived.
Therefore, the correct equation to relate amperes (I), watts (W), and volts (V) is:
[tex]\[ I = \frac{W}{V} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{1} \][/tex]
