Two lightbulbs, one with a rated power of 100 Watts and a second rated at 25 Wat

Question

Two lightbulbs, one with a rated power of 100 Watts and a second rated at 25 Watts, have filaments made of the same Tungsten filament which has a resistivity of 847 Ohm nm at the operating temperature of 2800 C. Each coiled filament has the same length of 56 cm. Assuming that each bulb is designed to be connected up to the same 120V DC source, .
(a) What is the resistance of the filament of the 100 W lightbulb? Correct: Your answer is correct. Ohms
(b) What is the resistance of the filament of the 25 W lightbulb?
Correct: Your answer is correct. Ohm
(c) What is the diameter of the filament of the 100 W lightbulb?
Incorrect: Your answer is incorrect.
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.

Explanation / Answer

(a) Resistance of the filament of 100W light bulb (R1)= 120*120 / 100 = 144 Ohms
(b) Resistance of the filament of 25W light bulb (R2)= 120*120/25 = 576 Ohms
(c)
Length of the filament = 56 cm
Resistivity = 847 * 10^-9 Ohm.m
R1 = l/A

144 = 847*10^-9 * .56 / A

on solving we get A = 3.3*10^-9

r1^2 = 3.3*10^-9

r1 = 32.38 m

(d)

Length of the filament = 56 cm
Resistivity = 847 * 10^-9 Ohm.m
R1 = l/A

576 = 847*10^-9 * .56 / A

on solving we get A = 8.23 * 10^-10

r2^2 = 8.23*10^-10

r1 = 16.19 m

(e) At room temperature resistivity = 5.64*10^-8 Ohm - nm

Resistance = 9.58 Ohms

V = IR

on solving for I we get 120/9.58 = 12.53 A

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