A 60W, 120V lightbulb contains a coiled tungsten filament that is 2.0m in length

Question

A 60W, 120V lightbulb contains a coiled tungsten filament that is 2.0m in length. The resistivity of tungsten is 5.28 ×10-8 ?·m at room temperature (20° C), and its temperature coefficient of resistivity is 0.0045 C°-1. The bulb's operating temperature is 3000C. Assume the bulb is in a circuit that supplies a 120 V potential difference across the light bulb and treat the light bulb as if it were a direct current (DC) device.

A) Assuming the filament has a circular cross-section, find the diameter of the filament.
B) Calculate the current flowing through the filament at operating temperature
C) As the filament heats up to its operating temperature, would the current be different at different temperatures? Explain your answer.

Explanation / Answer

Given Power of light bulb P = 60 W potential difference across the bolb V = 120 V Length of tungsten filament L = 2.0 m Resistivity of tungesten = 5.28*10-8 m Temperature coefficient of resistivity = 0.0045 Co-1    initial temperarue To = 20 o C Finial temperature T = 3000 o C Resistance of tungesten at room temperature is               P = V 2 / R              R = V 2 / P                 = ( 120 2 ) / 60                  = 240 Resistance of tungesten at 3000 o C is             R ' = R ( 1+ ( T - T o ) )                   = 240 ( 1 + (0.0045 Co-1 )(3000 -20))                   = 3458.4 A) The relation between resistance and resistivity of the material is             R ' = L / A               A = L / R '                   = (5.28*10-8 m )(2.0 m) / 3458.4                   = 0.00305 m 2                 r2 = 0.00305 m 2                 r = 0.0311 m Diameter of the filament                d = 2r                    = 2 ( 0.0311 m )                   = 0.0623 m __________________________________________________________ __________________________________________________________ B) current flowing through the filament at operating temperature
             I = V / R '                 = 120 V / 3458.4                 = 0.0346 A __________________________________________________________ __________________________________________________________ C) Yes , The filament heats up to its operating temperature the resistance of the filament increase . According to ohma law current is inversely proportional to resistance of the material .So current different at different teperatures.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.