Calculating Resistance for Cylindrical Shell Resistor

In summary, the conversation discusses the resistance of a copper cylindrical shell and a solid wire with the same length and resistance. The attempt at a solution presents incorrect equations for calculating resistance, which leads to the incorrect answer. The correct equations for this problem involve the cross-sectional area and the current flowing along the cylinder.
  • #1
CSGuy123
9
0

Homework Statement



A copper resistor has the shape of a cylindrical shell. What is the resistance of this resistor if its length is 1m, its inner radius is 0.1cm, and its outer radius is 0.2 cm? What is the radius of a solid wire of circular cross section with the same length and the same resistance?

The Attempt at a Solution



R = int(dR)
dR = (rho)dr / (2(pi)Lr)

R = int((rho)dr / (2(pi)Lr), from r1 to r2)
R =(rho)dr / (2(pi)L) * ln(r2/r1)

With the given info, I came to a resistance R of 1.8 x 10^-8 ohms, equivalent wire radius 0.55m, but apparently the correct answer is 1.8 x 10^-3 ohms, equivalent wire length 0.17 cm. I'm not sure what I'm doing wrong.

Thanks for the help again, guys!
 
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  • #2
Your equations don't look right for this problem at all. Maybe they're for current flowing out radially? This problem is much simpler: the current is flowing along the cylinder. (I admit that could be made clearer.) The resistance per unit length should be ρ/A, where A is the cross-sectional area.
 
  • #3
I had assumed that the current was flowing out radially. Apparently this textbook is notorious for being very vague on what exactly it wants. Thanks for the quick response!
 

1. What is a cylindrical shell resistor?

A cylindrical shell resistor is a type of electronic component that is used to regulate the flow of electrical current in a circuit. It consists of a cylindrical body made of a conductive material, such as metal, with a resistance element wrapped around its surface. When an electrical current passes through the resistor, it experiences a drop in voltage, thereby reducing the amount of current flowing through the circuit.

2. How does a cylindrical shell resistor work?

A cylindrical shell resistor works on the principle of Ohm's Law, which states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. When an electrical current passes through a cylindrical shell resistor, it encounters resistance in the form of the conductive material and the resistance element, causing a drop in voltage and regulating the flow of current.

3. What are the advantages of using a cylindrical shell resistor?

One of the main advantages of using a cylindrical shell resistor is its compact size, which allows it to be easily integrated into electronic circuits without taking up much space. Additionally, it has a high power handling capacity and can dissipate heat effectively, making it suitable for use in high-power applications. It also has a relatively low cost compared to other types of resistors.

4. What are the common applications of a cylindrical shell resistor?

Cylindrical shell resistors are commonly used in electronic devices and circuits, such as power supplies, amplifiers, and control systems. They are also used in automotive applications to regulate the flow of current in various systems, including the ignition, lighting, and charging systems. In industrial settings, they are used in equipment such as motors, generators, and transformers.

5. Can a cylindrical shell resistor be replaced with other types of resistors?

Yes, a cylindrical shell resistor can be replaced with other types of resistors, such as carbon composition, metal film, or wire-wound resistors. However, it is important to consider the specifications and requirements of the circuit before making a replacement. Different types of resistors have different characteristics, such as tolerance, power handling capacity, and temperature coefficient, which can affect the performance of the circuit.

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