To determine the current \( I \) in a circuit with a resistance of \( 25.0 \, \Omega \) and a power of \( 30.0 \, \text{W} \), we start with the given power formula:
[tex]\[ P = I^2 R \][/tex]
In this equation:
- \( P \) is the power in watts (\( 30.0 \, \text{W} \)),
- \( I \) is the current in amperes,
- \( R \) is the resistance in ohms (\( 25.0 \, \Omega \)).
We need to solve for the current \( I \). Rearrange the formula to isolate \( I \):
[tex]\[ I^2 = \frac{P}{R} \][/tex]
Now, substitute the given values for \( P \) and \( R \):
[tex]\[ I^2 = \frac{30.0}{25.0} \][/tex]
Calculate the right side:
[tex]\[ I^2 = 1.2 \][/tex]
To find \( I \), take the square root of both sides:
[tex]\[ I = \sqrt{1.2} \][/tex]
The calculated value of \( \sqrt{1.2} \) is approximately:
[tex]\[ I \approx 1.0954451150103321 \, \text{A} \][/tex]
So, the current in the circuit is approximately \( 1.09 \, \text{A} \). Thus, the correct answer is:
D. [tex]\( 1.09 \, \text{A} \)[/tex]
