Understanding Resistance in a Closed Loop
When a wire with a resistance of 10 ohms is bent into a closed circle, it presents an interesting scenario for understanding electrical resistance.
Resistance in a Closed Loop
- The total resistance of a closed loop is determined by the shape and dimensions of the wire.
- In a circular wire, the resistance does not change when it is bent; it remains 10 ohms.
Resistance Across the Diameter
- When measuring resistance across the diameter of the circle, we need to consider that the current can flow through two parallel paths.
- Each half of the wire, when divided by the diameter, has a resistance of 5 ohms (since the total resistance of the wire is 10 ohms).
Calculating Equivalent Resistance
- The two halves of the wire are in parallel when connected across the diameter.
- The formula for calculating the equivalent resistance (R_eq) in parallel is given by:
R_eq = (R1 * R2) / (R1 + R2)
- Substituting R1 = R2 = 5 ohms, we get:
R_eq = (5 * 5) / (5 + 5) = 25 / 10 = 2.5 ohms
Conclusion
- Therefore, when measuring the resistance across the diameter of the circle formed by the wire, the equivalent resistance is 2.5 ohms.
- This showcases how bending a wire into a circle can change the way we measure resistance depending on the pathways available for current flow.
By understanding the principles of resistance and parallel circuits, we can effectively analyze electrical circuits in various configurations.