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A [tex]$75 \Omega$[/tex] resistor in a circuit has a current flowing through it of [tex]2.0 A[/tex]. What is the power dissipated by the resistor? (Use [tex]P = I^2 R[/tex])

A. [tex]150 W[/tex]
B. [tex]300 W[/tex]
C. [tex]38 W[/tex]
D. [tex]450 W[/tex]

Sagot :

GinnyAnswer
To find the power dissipated by a resistor in a circuit, we can use the formula:

[tex]\[ P = I^2 \cdot R \][/tex]

where:
- [tex]\(P\)[/tex] is the power dissipated in watts (W),
- [tex]\(I\)[/tex] is the current in amperes (A),
- and [tex]\(R\)[/tex] is the resistance in ohms (Ω).

Given:
- The resistance [tex]\( R = 75 \Omega \)[/tex],
- and the current [tex]\( I = 2.0 A \)[/tex],

We will substitute these values into the formula to find the power [tex]\( P \)[/tex]:

1. First, square the current:
[tex]\[ I^2 = (2.0 \, A)^2 = 4.0 \, A^2 \][/tex]

2. Next, multiply the squared current by the resistance:
[tex]\[ P = I^2 \cdot R = 4.0 \, A^2 \cdot 75 \, \Omega \][/tex]

3. Perform the multiplication:
[tex]\[ P = 4.0 \cdot 75 = 300 \, W \][/tex]

Therefore, the power dissipated by the resistor is:

[tex]\[ 300 \, W \][/tex]

So, the correct answer is:

B. [tex]\(300 \, W\)[/tex]
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