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A circuit has a voltage drop of [tex][tex]$27 V$[/tex][/tex] across a [tex][tex]$30 \Omega$[/tex][/tex] resistor that carries a current of [tex][tex]$1.8 A$[/tex][/tex]. How much power is used by the resistor? Use [tex][tex]$P=VI$[/tex][/tex].

A. [tex][tex]$1.8 W$[/tex][/tex]
B. [tex][tex]$810 W$[/tex][/tex]
C. [tex][tex]$48.6 W$[/tex][/tex]
D. [tex][tex]$16.7 W$[/tex][/tex]



Answer :

GinnyAnswer
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]

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