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Resistance and Power
Name: Javen
Status: other
Grade: n/a
Location: Singapore
Date: April 4, 2011
Question:
Many books says Nichrome is used to make heating element formula P= V*V/R, when V is fixed, the power P dissipated would decreased if R is increased. So using high resistance conductor as heating element would not work as power dissipated is low. What is wrong with this argument?
Replies:
Javen
Here are the relevant formulas
V = I*R
P = V*I = V*(V/R) = (I*R)*I
There is nothing wrong with your argument.
Case 1: V = 10 Volts, Nichrome Resistor = 100 Ohms
Resulting current through the Nichrome Resistor = 0.1 Amps
Power dissipated in the Nichrome Resistor = 1 Watt
Case 2: V = 10 Volts, Nichrome Resistor = 1000 Ohms
Resulting current through the Nichrome Resistor = 0.01 Amps.
Power dissipated in the Nichrome Resistor = 0.1 Watts
Therefore increasing the resistance in the circuit reduces the dissipated
power.
I think you are missing the point in that you are assuming that "high
resistivity" means "higher resistivity" which leads you to think that that
leads to less power.
While "higher resistivity" will result in less power, "high resistivity" is
just a set resistance and is a means to install a high value resistor in the
circuit.
So how do we get a 60 Watt bulb and a 100 Watt bulb to output their
different powers on the same 115 volt house circuit?
The 60 Watt bulb incandescent (resistive) element will have a resistance of
0.5217 Ohms
The 100 Watt bulb incandescent (resistive) element will have a resistance of
0.8696 Ohms.
The 60 Watt bulb will output 115 V * 0.5217 A = 60 Watts
The 100 Watt bulb will output 115 V * 0.8696 A = 100 Watts
Sincere regards,
Mike Stewart
It is more a practical issue rather than a theoretical one. Low resistivity materials draw much more current/power than is usually desired, at least at household voltages (100-240 VAC). For example, a nichrome-based heater providing 1000 W of power consumes 8A at 125VAC. If you made the same heater out of copper wire, it would consume almost 500 A of current and fry everything (or blow the circuit breakers). Or you would have to use over 50 meters of copper wire, which is more expensive and difficult to build.
Even so, the resistivity is still often too low, given the power and size requirements. If you look inside a hair dryer, or old aquarium heaters, you may notice the nichrome wire is built as *coiled* wire, in order to increase its total resistivity in a small space.
Paul Bridges
Javen,
I think the answer relies on the temperature coefficient of Nichrome.
As you have stated, the Power decreases as the Resistance increases.
The temperature coefficient of Nichrome is 0.04% per degree C. This
means for every degree C increase, the Resistance increases by 0.04%.
In comparison to copper, the temperature coefficient of copper is
0.393% per degree C. So for every increase in C degrees, the
resistance in copper increases 0.393%.
So in essence, Nichrome would be a better choice for Power per degree
rise in Temperature.
-Alex Viray
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Update: June 2012
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