Answer :
To find the current in an electrical circuit where the power and resistance are known, we use the power formula and solve for the current:
[tex]\[ P = I^2 \cdot R \][/tex]
Let's denote:
- [tex]\( P \)[/tex] as the power, which is given as 15 watts.
- [tex]\( I \)[/tex] as the current, which we need to find.
- [tex]\( R \)[/tex] as the resistance, which is given as 100 ohms.
Rearrange the formula to solve for [tex]\( I \)[/tex]. First, isolate [tex]\( I^2 \)[/tex]:
[tex]\[ P = I^2 \cdot R \][/tex]
[tex]\[ I^2 = \frac{P}{R} \][/tex]
Substitute the given values for power and resistance into the equation:
[tex]\[ I^2 = \frac{15 \text{ watts}}{100 \text{ ohms}} \][/tex]
[tex]\[ I^2 = 0.15 \][/tex]
Now, take the square root of both sides to solve for [tex]\( I \)[/tex]:
[tex]\[ I = \sqrt{0.15} \][/tex]
[tex]\[ I \approx 0.387 \text{ amps} \][/tex]
Therefore, the current flowing through the circuit is approximately 0.387 amps. Looking at the given multiple choice options, the closest value is:
[tex]\[ \text{D. } 0.39 \text{ amps} \][/tex]
Thus, the current in a circuit that has a resistance of 100 ohms and a power of 15 watts is:
[tex]\[ D. \, 0.39 \text{ amps} \][/tex]
[tex]\[ P = I^2 \cdot R \][/tex]
Let's denote:
- [tex]\( P \)[/tex] as the power, which is given as 15 watts.
- [tex]\( I \)[/tex] as the current, which we need to find.
- [tex]\( R \)[/tex] as the resistance, which is given as 100 ohms.
Rearrange the formula to solve for [tex]\( I \)[/tex]. First, isolate [tex]\( I^2 \)[/tex]:
[tex]\[ P = I^2 \cdot R \][/tex]
[tex]\[ I^2 = \frac{P}{R} \][/tex]
Substitute the given values for power and resistance into the equation:
[tex]\[ I^2 = \frac{15 \text{ watts}}{100 \text{ ohms}} \][/tex]
[tex]\[ I^2 = 0.15 \][/tex]
Now, take the square root of both sides to solve for [tex]\( I \)[/tex]:
[tex]\[ I = \sqrt{0.15} \][/tex]
[tex]\[ I \approx 0.387 \text{ amps} \][/tex]
Therefore, the current flowing through the circuit is approximately 0.387 amps. Looking at the given multiple choice options, the closest value is:
[tex]\[ \text{D. } 0.39 \text{ amps} \][/tex]
Thus, the current in a circuit that has a resistance of 100 ohms and a power of 15 watts is:
[tex]\[ D. \, 0.39 \text{ amps} \][/tex]
