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 p(v, r) =

Explanation:

Step1: Write the variation equation

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

Step2: Find the value of $k$

Substitute $P = 20$, $V=10$, and $R = 5$ into the equation $P=\frac{k V^{2}}{R}$. We get $20=\frac{k\times10^{2}}{5}$. Simplify the right - hand side: $\frac{k\times100}{5}=20k$. So, $20k = 20$, and $k = 1$.

Step3: Write the power function

Substitute $k = 1$ back into the equation $P=\frac{k V^{2}}{R}$. The electric power as a function of voltage and electrical resistance is $P(V,R)=\frac{V^{2}}{R}$.

Answer:

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