Questions: The following equation expresses a relationship in terms of one variable. Which of the following identifies the equation in terms of a different variable? P=I × I × R (or P=P^2 R) I=? a. R^2/P b. P^2/R c. sqrt(R/P) d. sqrt(P/R)

The following equation expresses a relationship in terms of one variable. Which of the following identifies the equation in terms of a different variable?

P=I × I × R (or P=P^2 R)
I=?

a. R^2/P
b. P^2/R
c. sqrt(R/P)
d. sqrt(P/R)
Transcript text: The following equation expresses a relationship in terms of one variable. Which of the following identifies the equation in terms of a different variable? \[ \begin{array}{l} P=I \times I \times R\left(\text { or } P=P^{2} R\right) \\ I=? \end{array} \] a. $\frac{R^{2}}{P}$ b. $\frac{P^{2}}{R}$ c. $\sqrt{\frac{R}{P}}$ d. $\sqrt{\frac{P}{R}}$
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Solution

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Solution Steps

Step 1: Understand the Given Equation

The given equation is: \[ P = I^2 R \] We need to solve for \( I \).

Step 2: Isolate the Variable \( I \)

To isolate \( I \), we start by dividing both sides of the equation by \( R \): \[ \frac{P}{R} = I^2 \]

Step 3: Solve for \( I \)

Next, take the square root of both sides to solve for \( I \): \[ I = \sqrt{\frac{P}{R}} \]

Step 4: Identify the Correct Option

Compare the derived expression for \( I \) with the given options: a. \(\frac{R^2}{P}\) b. \(\frac{P^2}{R}\) c. \(\sqrt{\frac{R}{P}}\) d. \(\sqrt{\frac{P}{R}}\)

The correct option is: \[ \boxed{d. \sqrt{\frac{P}{R}}} \]

Final Answer

\[ \boxed{d. \sqrt{\frac{P}{R}}} \]

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