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

Answer:

The power drawn by the toaster is closest to:

(A) 370 W

Explanation:

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

$R=\frac{pL}{A} =\frac{pL}{\pi r^{2} }$

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

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

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

$P=\frac{V^2}{R} =\frac{120^2}{38.7940} =371.191 Watts$