Chapter 26, Problem 047 A heating element is made by maintaining a potential dif

Question

Chapter 26, Problem 047 A heating element is made by maintaining a potential difference of 87.0 V across the length of a Nichrome wire that has a 3.36 × 10–6 m2 cross section. Nichrome has a resistivity of 5.00 × 10–7 ·m. (a) If the element dissipates 2100 W, what is its length? (b) If 116 V is used to obtain the same dissipation rate, what should the length be?


Chapter 26, Problem 047 A heating element is made by maintaining a potential difference of 87.0 V across the length of a Nichrome wire that has a 3.36 × 10–6 m2 cross section. Nichrome has a resistivity of 5.00 × 10–7 ·m. (a) If the element dissipates 2100 W, what is its length? (b) If 116 V is used to obtain the same dissipation rate, what should the length be?


Chapter 26, Problem 047 A heating element is made by maintaining a potential difference of 87.0 V across the length of a Nichrome wire that has a 3.36 × 10–6 m2 cross section. Nichrome has a resistivity of 5.00 × 10–7 ·m. (a) If the element dissipates 2100 W, what is its length? (b) If 116 V is used to obtain the same dissipation rate, what should the length be?

Explanation / Answer

a] Power P = V^2/R

            R = V^2/P = 87^2/2100 = 3.604 ohm

       L = R*A/rho = 3.604*3.36e-6/5e-7 = 24.2 m

b] L = [ V^2/P]*A/rho = [116^2/2100]*3.36e-6/5e-7 = 43.05 m

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