Question

The heater element of a 120 V toaster is a 5.4 m length of nichrome wire, whose diameter is 0.48 mm. The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 Ω·m. The toaster is operated at a voltage of 120 V. The power drawn by the toaster is closest to:

(A) 370 W
(B) 360 W
(C) 380 W
(D) 400 W
(E) 410 W

Answer 1

The power drawn by the toaster is closest to:

(A) 370 W

Step-by-step explanation:

First we calculate the resistance of the nichrome wire (R).

`R=(pL)/(A) =(pL)/(\pi r^(2) ) \\`

Where radious (r), resistance coefficient (p), and Length (L)

`r=(0.48)/(2) 10^(-3) m\\\\L=5.4 m\\p=1.3*10^(-3)\varOmega  \\\\\\Replacing:\\\\R=(1.3(10)^(-6) *5.4)/(\pi* 0.24^(2) (10)^(-6)) =38.7940`

After replace the value in the ohm law power formula to obtain the power consumed:

`P=(V^2)/(R) =(120^2)/(38.7940) =371.191 Watts`