Question

You are designing a toaster heating element to consume 10A at 120V. The heating element will be made from a length of cylindrical nichrome wire having a uniform diameter of 0.8mm. Nichrome has a resistivity (⍴) of 1.6 x 10-6 Ωm. a. What resistance does this wire need to have? b. How long does the wire need to be? c. If the toaster is operated for 5 minutes, how much energy is consumed? 2)

Answer 1

Answer: a) 12 Ω; b)  15.10 m; c) 360 kJ

Explanation: In order to explain this problem we have to considere the OHM law which is given by:

V=R*I where R is the resistance and I the current, V is the voltage.

For the toaster heating the resistance must be equal

R=V/I=120/10= 12 Ω

We also know that R=ρ*L/A where L and A are the length and area of the wire.

Then the length of the wire is given by:

L=R*A/ρ= 12*π*(0.8*10^-3)^2/1.6*10^-6=15.10 m

Finally we can calculate the consumed energy  by the toaster heating during 5 minutes (5*60s=300 s).

The power is equal:

P=I*V= 10*120=1200 W

E= P*time (s)= 1200*300=360*10^3J

Answer 2

Answer:

a) 12 Ω; b)  3.77 m; c) 360 kJ

Explanation:

In order to explain this problem we have to consider the OHM law which is given by:

V=R*I where R is the resistance and I the current, V is the voltage.

For the toaster heating the resistance must be equal

R=V/I=120/10= 12 Ω

We also know that R=ρ*L/A where L and A are the length and area of the wire.

Then the length of the wire is given by:

L=R*A/ρ= 12*π*(0.4*10^-3)^2/1.6*10^-6= 3.77 m

Finally we can calculate the consumed energy  by the toaster heating during 5 minutes (5*60s=300 s).

The power is equal:

P=I*V= 10*120=1200 W

E= P*time (s)= 1200*300=360*10^3J