Question

There is a 120 V circuit in a house that is a dedicated line for the dishwasher, meaning the dishwasher is the only resistor on that circuit line. If the dishwasher draws 18 A of electricity, what would the resistance of the dishwasher be? Round the answer to the nearest hundredth of an ohm.

Answer 1

To find the resistance of the dishwasher, we can use Ohm's Law, which is given by the formula:

\[
V = I \times R
\]

where:
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).

We can rearrange this formula to solve for resistance (\( R \)):

\[
R = \frac{V}{I}
\]

Given:
- \( V = 120 \) V,
- \( I = 18 \) A,

we can substitute these values into the formula:

\[
R = \frac{120 \, \text{V}}{18 \, \text{A}}
\]

Calculating this gives:

\[
R = \frac{120}{18} \approx 6.6667 \, \text{ohms}
\]

Rounding this to the nearest hundredth, we get:

\[
R \approx 6.67 \, \text{ohms}
\]

Thus, the resistance of the dishwasher is approximately **6.67 ohms**.