Question

the electric power varies directly as the square of the voltage (v) and inversely as the electrical resistance (r). if the voltage is 10 volts and the electrical resistance is 5 ohms, then the electric power is 20 watts. express the electric power as a function of voltage and electrical resistance. answer 2 points keypad keyboard shortcuts p(v, r) =

Explanation:

Step1: Set up the variation equation

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

Step2: Find the value of \(k\)

Given \(V = 10\) volts, \(R=5\) ohms, and \(P = 20\) watts. Substitute these values into \(P=\frac{kV^{2}}{R}\):
\(20=\frac{k\times10^{2}}{5}\)
\(20=\frac{100k}{5}\)
\(20 = 20k\), so \(k = 1\)

Step3: Write the function

Substitute \(k = 1\) into \(P=\frac{kV^{2}}{R}\), we get \(P(V,R)=\frac{V^{2}}{R}\)

Answer:

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