To determine how much power is used by the resistor, we can use 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).
Given the data:
- Voltage drop ([tex]\( V \)[/tex]) = 27 volts,
- Current ([tex]\( I \)[/tex]) = 1.8 amperes.
Substituting the given values into the formula, we have:
[tex]\[ P = 27 \, \text{V} \times 1.8 \, \text{A} \][/tex]
When we multiply these values:
[tex]\[ P = 48.6 \, \text{W} \][/tex]
Thus, the power used by the resistor is:
[tex]\[ 48.6 \, \text{W} \][/tex]
Among the given answer choices:
- A. [tex]\(1.8 \, \text{W}\)[/tex]
- B. [tex]\(810 \, \text{W}\)[/tex]
- C. [tex]\(48.6 \, \text{W}\)[/tex]
- D. [tex]\(16.7 \, \text{W}\)[/tex]
The correct answer is:
[tex]\[ \boxed{48.6 \, \text{W}} \][/tex]
