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The power in an electrical circuit is given by the equation [tex]P = I^2 R[/tex], where [tex]I[/tex] is the current flowing through the circuit and [tex]R[/tex] is the resistance of the circuit. What is the current in a circuit that has a resistance of 30 ohms and a power of 2 watts?

A. 15 amps
B. 3.9 amps
C. 0.067 amps
D. 0.26 amps


Sagot :

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]