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)
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. $\sqrt{\frac{P}{R}}$
Solution
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:
\[
\boxed{d. \sqrt{\frac{P}{R}}}
\]