Ch. 26
26.
(III) You are designing a wire resistance heater to heat an enclosed volume of gas. For the
apparatus to function properly, this heater must transfer heat to the gas at a very constant rate.
While in operation, the resistance of the heater will always be close to the value
0
,
RR
but
may fluctuate slightly causing its resistance to vary a small amount
R
D
0
R.
To maintain
the heater at constant power, you design the circuit shown in Fig. 26
–
44, which includes two
resistors, each of resistance
r
. Determine the value for
r
so that the heater power will remain
constant even if its resistance
R
fluctuates by a small amount. [
Hint:
If
0
,
D
then
0
dP
P
R
.
dR
DD
<
0
]
[Solution]
The goal is to determine
r
so that
0
0.
R
dP
dR
This ensures that
R
produce very little change in
,
R
P
since
.
R
R
dP
PR
dR
The power delivered to the heater can be found by
2
heater
heater
,
P
V
R
and so we need to determine the
voltage across the heater.
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 Fall '10
 MichaelChen
 Resistance, Heat, Resistor, Electrical resistance, Voltage drop

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