Calculating Copper Wire Diameter Based on Resistance
What is the relationship between the resistance of a copper wire and its diameter?
The resistance, R (ohms) of a copper wire of fixed length is inversely proportional to the square of its diameter, d mm.
Understanding the Relationship:
Electrical Resistance: Electrical resistance is a fundamental concept in physics that describes how materials impede the flow of electric current. In the case of a copper wire, the resistance is affected by the wire's diameter. Inversely Proportional Relationship: When it comes to copper wire, the resistance is inversely proportional to the square of its diameter. This means that as the diameter of the wire increases, the resistance decreases, and vice versa. Mathematical Representation: The relationship can be expressed by the equation R = k/d², where R is the resistance, d is the diameter, and k is a constant. This formula allows us to calculate the diameter of a wire based on its resistance. Given Data Example: For example, if we have a copper wire with a diameter of 2.5 mm and a resistance of 20 ohms, we can determine the constant, k, to use in the formula. Now, let's move on to the specific question regarding the diameter of a wire with a resistance of 31.25 ohms.What is the diameter of a copper wire with a resistance of 31.25 ohms?
Final answer: The physics concept of electrical resistance is used to determine the difference in diameter of two copper wires with different resistances. Given a resistance value of 31.25 ohms and a constant determined from an initial diameter and resistance, the new diameter found is 2 mm.