Answer :
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."
[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."
