Nichrome Resistor and Copper wire

In summary, the conversation discusses a homework problem involving a 10 ohms Nichrome resistor and copper leads in an electronic circuit. The question posed is what change in temperature would cause the resistance of the Nichrome wire to be equal to the resistance of the copper leads. The equations RCu = 0.03[1 + aCu(tC – 20)] and change in Rw = 10aw(tC – 20) are given to solve for tC, with aCu and aw being constants at 20 degrees C. The individual attempting to solve the problem initially got an answer of 30.6 C but it was incorrect.
  • #1
hime
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Homework Statement


A 10 ohms Nichrome resistor is wired into an electronic circuit using copper leads (wires) of diameter 0.6 mm with a total length of 50 cm. The additional resistance is due to the copper leads is 0.03 ohms.

What change in temperature would produce a change in resistance of the Nichrome-wire equal to the resistance of the copper leads?

Homework Equations



RCu = 0.03[1 + aCu(tC – 20)]= change in Rw = 10aw(tC – 20); solve for tC
aCu at 20 degree C= 3.9 x 10^-3
aw at 20 degree C = 4.3 x 10^-3

The Attempt at a Solution



0.03[1 + aCu(tC – 20)] = 10aw(tC – 20)
I solved for tc and got 30.6 C but it is not the right answer so please help.
 
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  • #2
Welcome to PF :smile:

30.6 C does not solve the last equation you wrote. There must have been some algebra error made after that.

You are on the right track, try again. You can check your answer by substituting it into your equation,
0.03[1 + aCu(tC – 20)] = 10aw(tC – 20)
 
  • #3


To find the change in temperature that would produce a change in resistance of the Nichrome-wire equal to the resistance of the copper leads, we can use the equation RCu = 0.03[1 + aCu(tC – 20)] = change in Rw = 10aw(tC – 20). Plugging in the values given, we get 0.03[1 + (3.9 x 10^-3)(tC – 20)] = 10(4.3 x 10^-3)(tC – 20). Solving for tC, we get tC = 29.3 degrees Celsius. However, this answer may not be correct as it depends on the accuracy of the given values for aCu and aw. It is also important to note that this calculation assumes that the temperature change affects both the Nichrome resistor and the copper leads equally. In reality, the temperature change may affect the two materials differently and the answer may vary. Further testing and experimentation may be necessary to accurately determine the change in temperature that would produce an equal change in resistance for the Nichrome-wire and copper leads.
 

1. What is the purpose of a nichrome resistor?

A nichrome resistor is a type of resistor made from a nickel-chromium alloy. Its purpose is to resist the flow of electric current in a circuit, thereby controlling the amount of current that passes through it. This makes it useful for regulating the amount of heat or voltage in a circuit.

2. How does a nichrome resistor work?

A nichrome resistor works by using the properties of the nickel-chromium alloy to resist the flow of electric current. As current passes through the resistor, the alloy material heats up, which in turn increases its resistance. This allows the resistor to regulate the amount of current in the circuit.

3. What are the advantages of using a nichrome resistor?

There are several advantages to using a nichrome resistor, including its high melting point, good stability at high temperatures, and low temperature coefficient of resistance. It also has a high resistance per unit length, making it useful for applications where a high resistance is needed in a small space.

4. How is a copper wire different from a nichrome resistor?

Copper wire is a type of conductor that allows electricity to flow through it with little resistance. In contrast, a nichrome resistor is designed to resist the flow of electricity and convert it into heat. Additionally, copper is a good conductor of heat, while nichrome has a higher resistance to heat.

5. What are common applications for nichrome resistors and copper wire?

Nichrome resistors are commonly used in heating elements, such as in electric stoves and hair dryers, as well as in electronic devices to regulate voltage. Copper wire is used in a wide range of applications, including electrical wiring, motors, and electronic circuits, due to its high conductivity.

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