Chapter 8.1, Problem 17P

To determine

To find the current that will develop $1.6$ kilowatts of power.

Answer to Problem 17P

The magnitude of current required is $2$ amperes.

Explanation of Solution

Given information:

The given statement is:

“The power developed by an electric current varies directly as the square of the magnitude of the current. If a current of $0.5$ amperes develops $100$ watts of power, what current will develop $1.6$ kilowatts of power?”

Calculation :

The magnitude of current can be calculated by:

  $\begin{array}{l}\frac{y_1}{x_1{}^2}=\frac{y_2}{x_2{}^2}\\ \frac{100}{{0.5}^2}=\frac{1600}{x_2{}^2}\left[1.6\text{ kilowatts}=1600\text{ watts}\right]\\ x_2{}^2=\frac{1600\times 0.25}{100}\\ x_2{}^2=4\\ x_2=\sqrt{4}\\ x_2=2\end{array}$

Hence, the magnitude of current required is $2$ amperes.