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

Answer:

$P=V^2/R$

$R=V^2/P$

Upon substituting the values

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

   Also

   R=ρ*L/A

   L=R*A/ρ

   L=$\frac{0.72*3.73*10^-6 }{5*10^-7}$ = 5.44m

b) when the voltage 107 is used

    R=107*107/7800 = 1.468OHM

     L=$\frac{1.468*3.73*10^-6 }{5*10^-7}$ =11.1m