Robert Cinca - Physics
Part
Part 1:
1: Logical
Logical Argument
Argument
Logical argument to find the functionality of the relationship between the final current
Logical argument to find the functionality of the relationship between the final current
and the surge current time:
and the surge current time:
For a filament bulb to emit light, the tungsten filament needs to be heated to a
For a filament bulb to emit light, the tungsten filament needs to be heated to a
sufficiently large temperature for it to glow white hot.
sufficiently large temperature for it to glow white hot.
The net energy, , required to raise the temperature of the filament to its equilibrium
The net energy, , required to raise the temperature of the filament to its equilibrium
temperature is related to
for a fixed mass, , where is the specific heat
temperature is related to
for a fixed mass, , where is the specific heat
capacity of tungsten and
is the change in temperature.
capacity of tungsten and
is the change in temperature.
The resistivity of tungsten varies with temperature and the data is taken from “Resistivity of
The resistivity of tungsten varies with temperature
and the data is taken from “Resistivity of
Tungsten” (see appendix for resistivity values) 5 5 suggests:
Tungsten” (see appendix for resistivity values) suggests:
(as
(as
Then
Then
.
.
(where
(where
is much greater than ).
is much greater than ).
is the resistivity at room temperature).
is the resistivity at room temperature).
Now the energy required, , is in the order of the product of the final power input, , and
Now the energy required, , is in the order of the product of the final power input, , and
the surge current time, .
the surge current time, .
,
The final power, , may be given by
,
The final power, , may be given by
where is the final current and the final resistance at the equilibrium temperature.
where is the final current and the final resistance at the equilibrium temperature.
So the energy required, , is:
So the energy required, , is:
(as
for a fixed length and cross-sectional area of wire)
(as
for a fixed length and cross-sectional area of wire)
From above, as
From above, as
giving
giving
so
so
.
.
Now
Now
(where
(where
)
)
Experimentally
. The range is due to the final temperatures of the bulb being
Experimentally
. The range is due to the final temperatures of the bulb being
approximately between 2000K and 3000K 5 5 .
approximately between 2000K and 3000K .
Taking
Taking
(
(
)
)
(where
(where
is a constant)
is a constant)
5
5
“Resistivity of Tungsten”, The Physics Factbook [Online][Date Accessed 13/06/13] URL:
“Resistivity of Tungsten”, The Physics Factbook [Online][Date Accessed 13/06/13] URL:
http://hypertextbook.com/facts/2004/DeannaStewart.shtml (Elert, 2004)
http://hypertextbook.com/facts/2004/DeannaStewart.shtml (Elert, 2004)
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