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Rewrite the formula to find voltage.

The formula for electrical power (\(P\), in watts) is \( P = \frac{V^2}{R} \), where \(V\) is the voltage in volts and \(R\) is the resistance in ohms. For a particular brand of water heater, \(R\) is 32 ohms and \(P\) is 0.5 watts.

The formula to find [tex]\(V\)[/tex] is [tex]\(\square\)[/tex], and the voltage at which the heater operates is [tex]\(\square\)[/tex] volts.

Sagot :

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To solve for the voltage \( V \) given the power \( P \) and resistance \( R \), we start with the formula for electrical power:

[tex]\[ P = \frac{V^2}{R} \][/tex]

We need to isolate \( V \) in this equation. Begin by multiplying both sides of the equation by \( R \) to get rid of the denominator:

[tex]\[ P \times R = V^2 \][/tex]

Next, solve for \( V \) by taking the square root of both sides:

[tex]\[ V = \sqrt{P \times R} \][/tex]

Therefore, the formula to find \( V \) is:

[tex]\[ V = \sqrt{P \times R} \][/tex]

Given that \( P = 0.5 \) watts and \( R = 32 \) ohms, substituting these values into the formula yields:

[tex]\[ V = \sqrt{0.5 \times 32} \][/tex]

Calculating the value inside the square root:

[tex]\[ 0.5 \times 32 = 16 \][/tex]

Thus, the formula simplifies to:

[tex]\[ V = \sqrt{16} \][/tex]

Finally, calculating the square root of 16 gives:

[tex]\[ V = 4.0 \][/tex]

So the completed answer is:
"The formula to find [tex]\( V \)[/tex] is [tex]\( V = \sqrt{P R} \)[/tex], and the voltage at which the heater operates is 4.0 volts."
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