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 3.83 × 10–6 m2 cross section. Nichrome has a resistivity of 5.00 × 10–7 Ω·m. (a) If the element dissipates 5200 W, what is its length? (b) If 120 V is used to obtain the same dissipation rate, what should the length be?

Answer 1

Answer:

Explanation:

power of a heating element = V² / R where V is voltage and R is resistance

putting in the values

5200 = 75² / R

R = 1.082 ohm

Formula for resistance

R = ρ L / S , ρ is resistivity , L is length and S is cross sectional area

1.082 = 5 x 10⁻⁷ x L / (3.83 x 10⁻⁶)

L = 8.29 m

b )

power of a heating element = V² / R , R is new resistance

5200 = 120² / R

R = 2.77 ohm

R = ρ L / S , ρ is resistivity , L is length and S is cross sectional area

2.77 = 5 x 10⁻⁷ x L / (3.83 x 10⁻⁶)

L = 21.22 m