Question

the electric power varies directly as the square of the voltage (v) and inversely as the electrical resistance (r). if the voltage is 12 volts and the electrical resistance is 3 ohms, then the electric power is 48 watts. express the electric power as a function of voltage and electrical resistance.

Explanation:

Step1: Write the general variation equation

Since the electric power \(P\) varies directly as the square of the voltage \(V\) and inversely as the electrical resistance \(R\), the general equation is \(P = k\frac{V^{2}}{R}\), where \(k\) is the constant of variation.

Step2: Substitute the given values to find \(k\)

Given \(V = 12\) volts, \(R=3\) ohms, and \(P = 48\) watts. Substitute into \(P = k\frac{V^{2}}{R}\):
\(48=k\frac{12^{2}}{3}\)
First, calculate \(12^{2}=144\), then \(\frac{144}{3} = 48\). So the equation becomes \(48=k\times48\). Solving for \(k\), we divide both sides by \(48\), and get \(k = 1\).

Step3: Write the final function

Substitute \(k = 1\) back into \(P = k\frac{V^{2}}{R}\). The function is \(P=\frac{V^{2}}{R}\)

Answer:

\(P=\frac{V^{2}}{R}\)