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The power in an electrical circuit is given by the equation [tex]P = I^2 R[/tex], where [tex]I[/tex] is the current flowing through the circuit and [tex]R[/tex] is the resistance of the circuit. What is the power in a circuit that has a current of [tex]12 \, \text{amps}[/tex] and a resistance of [tex]100 \, \text{ohms}[/tex]?

A. 8.3 watts
B. 14,400 watts
C. 144 watts
D. 1200 watts

Sagot :

GinnyAnswer
To determine the power ([tex]\(P\)[/tex]) in an electrical circuit using the given current ([tex]\(I\)[/tex]) and resistance ([tex]\(R\)[/tex]), we utilize the power formula:
[tex]\[ P = I^2 \times R \][/tex]

Given:
- Current ([tex]\(I\)[/tex]) is 12 amps.
- Resistance ([tex]\(R\)[/tex]) is 100 ohms.

Let's go through the step-by-step solution:

1. Calculate [tex]\( I^2 \)[/tex] (the square of the current):
[tex]\[ I^2 = 12^2 = 144 \][/tex]

2. Multiply [tex]\( I^2 \)[/tex] by the resistance [tex]\( R \)[/tex]:
[tex]\[ P = 144 \times 100 = 14,400 \][/tex]

Therefore, the power [tex]\(P\)[/tex] in the circuit is [tex]\(14,400\)[/tex] watts.

The correct answer is:
B. 14,400 watts
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