Physics2 HW help? ( Easy steps will be ok, understanding, thank you) We are give
ID: 1443740 • Letter: P
Question
Physics2 HW help? ( Easy steps will be ok, understanding, thank you)
We are given the following data for Tungsten: resistivity = 5.51 times 10^-8 ohm m temperature coefficient of resistivity = 0.0045 (C)^-1. At a temperature of 20 degree C, a thin Tungsten filament (in the form of a solid cylindrical wire) has a length of 0.5 m and a constant circular cross section with a diameter of 0.5 mm. A potential difference of 15 volts is applied across its ends. At a temperature of 20 degrees C, what is the filament's resistance? At a temperature of 20degree C, what is the current and power dissipation in the filament? Now, suppose that the Tungsten filament reaches a steady state operating temperature of 300 degrees C? What potential difference is required to maintain the same current in the filament as that at 20degrees C? What potential difference is required to maintain the same power dissipation in the filament as that at 20 degrees C?Explanation / Answer
a)
Area
A=pi*D2/4 =pi*(0.5*10-3)2/4
A=1.963*10-7 m2
Resistance of tungsten filament at T=20oC is
R=pL/A =(5.51*10-8)*0.5/(1.963*10-7)
R=0.14 ohms
b)
Current through the filament is
I=V/R =15/0.14 =107 A (approx)
Power dissipated in filament
P=V2/R =152/0.14 =1607 Watts
c)
Resistance as a function of temperature is given by
R=Ro[1+alpha*(T-To)]
R=0.14[1+0.0045(300-20)]
R=0.3164 ohms
Potential difference across the filament to maintain the same temperature is
V=IR =107*0.3164
V=33.85 Volts
d)
P=V2/R
=>V=sqrt[PR] =sqrt[1607*0.3164[
V=22.55 Volts