To find the current in a circuit given the power and resistance, we'll use the formula for electrical power:
[tex]\[ P = I^2 \times R \][/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 are given:
- [tex]\( P = 2 \)[/tex] watts
- [tex]\( R = 30 \)[/tex] ohms
Our goal is to find the current [tex]\( I \)[/tex]. We start by rearranging the formula to solve for [tex]\( I \)[/tex]:
[tex]\[ P = I^2 \times R \][/tex]
[tex]\[ I^2 = \frac{P}{R} \][/tex]
[tex]\[ I = \sqrt{\frac{P}{R}} \][/tex]
Now we substitute the given values into the equation:
[tex]\[ I = \sqrt{\frac{2}{30}} \][/tex]
Calculating the fraction inside the square root:
[tex]\[ \frac{2}{30} = \frac{1}{15} \][/tex]
So the equation now is:
[tex]\[ I = \sqrt{\frac{1}{15}} \][/tex]
Taking the square root:
[tex]\[ I \approx 0.2582 \][/tex]
Therefore, the current in the circuit is approximately [tex]\( 0.2582 \)[/tex] amps. Among the given options:
A. 15 amps
B. 3.9 amps
C. 0.067 amps
D. 0.26 amps
The correct answer is:
[tex]\[ \boxed{0.26 \text{ amps}} \][/tex]
