Question 99f82

Jul 6, 2015

The operating resistance is $60 \Omega$.
The operating current is $\text{4 A}$.

Explanation:

To determine your washing machine's operating resistance you need to combine the formula for power with the equation for Ohm's Law.

Electric power is defined as the total work done per second by a current passing through a potential difference

$P = I \cdot V$

Ohm's Law states that the current passing through a conductor is directly proportional to the potential difference applied to that conductor

$I = \frac{V}{R}$, where

$R$ - the resistance of the conductor.

Use the equation for Ohm's Law and replace the current, $I$, in the equation for electric power

$P = {\underbrace{I}}_{\textcolor{b l u e}{= \text{V"/"R}}} \cdot V = {V}^{2} / R$

This means that the resistance will be equal to

R = V^2/P = (240""^2)/960 "V"^2/"W" = 57600/960 * V^(cancel(2))/(cancel(V) * A)

R = 60underbrace("V"/"A")_(color(blue)("=ohm")) = color(green)(60 Omega)#

Use this value in the equation for Ohm's Law to determine the operating current current in normal use

$I = \frac{V}{R} = \left(\text{240 V")/(60Omega) = color(green)("4 A}\right)$