To determine the current flowing through the circuit, we start with the power equation for an electrical circuit:
[tex]\[ P = I^2 R \][/tex]
where:
- [tex]\( P \)[/tex] is the power in watts (W)
- [tex]\( I \)[/tex] is the current in amperes (A)
- [tex]\( R \)[/tex] is the resistance in ohms (Ω)
We need to solve for the current [tex]\( I \)[/tex]. Rearranging the power equation to solve for [tex]\( I \)[/tex]:
[tex]\[ I^2 = \frac{P}{R} \][/tex]
[tex]\[ I = \sqrt{\frac{P}{R}} \][/tex]
Substituting the given values into the equation:
- [tex]\( P = 2.00 \, \text{W} \)[/tex]
- [tex]\( R = 30.0 \, \Omega \)[/tex]
[tex]\[ I = \sqrt{\frac{2.00}{30.0}} \][/tex]
Now, let's calculate it step-by-step.
1. First, perform the division inside the square root:
[tex]\[ \frac{2.00}{30.0} = 0.0667 \][/tex]
2. Next, take the square root of the result:
[tex]\[ I = \sqrt{0.0667} \approx 0.258 \, \text{A} \][/tex]
Thus, the current in the circuit is approximately [tex]\( 0.258 \)[/tex] A.
So, the correct answer is:
C. 0.258 A
