Question

While Dr. Chesnutt is making breakfast, she turns on her 1060 W toaster, 500 W coffee pot, and 1230 W microwave at the same time. Part Description Answer Save Status A. If all three appliances are connected in parallel across a 120 V power source, what total current would they draw from the source? (include units with answer) Format Check Click here to check your answer 4 pts.100% 13% try penalty 8 try limit # tries: 0

Answer 1

Answer:23.25 A

Explanation:

Given

Rating of toaster $P_1=1060\ W$

Coffee pot $P_2=500\ W$

microwave $P_3=1230\ W$

Voltage applied $V=120\ V$

if they are connected in parallel then all three operates at same voltage

so their resistance are

$P=\frac{V^2}{R}$

thus $R_1=\frac{V^2}{P_1}=\frac{120^2}{1060}$

$R_1=13.58\ \Omega$

$R_2=\frac{V^2}{P_2}=\frac{120^2}{500}$

$R_2=28.8\ \Omega$

$R_3=\frac{V^2}{P_3}=\frac{120^2}{1230}$

$R_3=11.707\ \Omega$

and $V=IR$

where I=current

thus $I_1=\frac{V}{R_1}=\frac{120}{13.58}$

$I_1=8.83\ A$

$I_2=\frac{V}{R_2}=\frac{120}{28.8}$

$I_2=4.16\ A$

$I_3=\frac{V}{R_3}=\frac{120}{11.707}$

$I_3=10.25\ A$

Total current $I=I_1+I_2+I_3=23.24\ A$