Question

using a multimeter with hold capabilities, you see that the startup current for the saw is 12 a. you look at the breaker and note that its rated for 20 a (peak). if the peak current of the shop light is 2.828 a, how many shop lights can be running when the saw is started?

Explanation:

Step1: Calculate the available current for shop lights

The breaker is rated for \(20\ A\) (peak) and the startup current for the saw is \(12\ A\). So the available current for shop lights is \(I_{available}=20 - 12=8\ A\)

Step2: Calculate the RMS current of a shop light

For a sinusoidal current, the relationship between peak current \(I_{peak}\) and RMS current \(I_{rms}\) is \(I_{rms}=\frac{I_{peak}}{\sqrt{2}}\). Given \(I_{peak} = 2.828\ A\), then \(I_{rms}=\frac{2.828}{\sqrt{2}}\approx2\ A\)

Step3: Calculate the number of shop lights

Let \(n\) be the number of shop lights. Using the formula \(n=\frac{I_{available}}{I_{rms}}\). Substitute \(I_{available} = 8\ A\) and \(I_{rms}=2\ A\) into the formula, we get \(n=\frac{8}{2}=4\)

Answer:

\(4\)