Question

A heating element is made by maintaining a potential difference of 75.0 V across the length of a Nichrome wire that has a 3.73 × 10–6 m2 cross section. Nichrome has a resistivity of 5.00 × 10–7 Ω·m. (a) If the element dissipates 7880 W, what is its length? (b) If 107 V is used to obtain the same dissipation rate, what should the length be?

Answer 1

`P=V^2/R`

`R=V^2/P`

Upon substituting the values

a) R= 75*75/7800 = 0.72ohm

Also

R=ρ*L/A

L=R*A/ρ

L=
`(0.72*3.73*10^-6 )/(5*10^-7)` = 5.44m

b) when the voltage 107 is used

R=107*107/7800 = 1.468OHM

L=
`(1.468*3.73*10^-6 )/(5*10^-7)` =11.1m