Two wires of same metal an have a same length but there are cross sect...
Given:
- Two wires of the same metal have the same length.
- The cross-sectional areas of the wires are in the ratio of 3:1.
- The resistance of the thicker wire is 10 ohms.
To find:
- The resistance of the thinner wire.
Solution:
Step 1: Understanding the Concept of Resistance
Resistance is a physical property of a material that determines the opposition to the flow of electric current. It is denoted by the symbol "R" and is measured in ohms (Ω).
The resistance of a wire depends on three factors:
1. Length: Longer wires have higher resistance.
2. Cross-sectional Area: Wires with larger cross-sectional areas have lower resistance.
3. Resistivity: This is a property of the material and determines how strongly it resists the flow of electric current.
Step 2: Relationship Between Resistance, Length, and Cross-sectional Area
The resistance of a wire can be calculated using the formula:
R = (ρ * L) / A
where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
From the given information, we know that the length of both wires is the same. Let's assume it to be "L".
Step 3: Applying the Given Information
Given that the cross-sectional areas of the wires are in the ratio of 3:1, we can assume the cross-sectional area of the thicker wire to be 3x and the cross-sectional area of the thinner wire to be x.
It is also given that the resistance of the thicker wire is 10 ohms. Let's assume the resistivity of the metal to be "p".
Using the resistance formula, we can write the equation for the thicker wire as:
10 = (p * L) / (3x)
Step 4: Solving for the Resistance of the Thinner Wire
To find the resistance of the thinner wire, we need to find the value of "x" in the equation. We can do this by rearranging the equation as follows:
10 = (p * L) / (3x)
10 * 3x = p * L
30x = p * L
Now, let's substitute the value of "x" into the equation for the resistance of the thinner wire:
R = (p * L) / x
R = (30x * L) / x
R = 30L
Therefore, the resistance of the thinner wire is 30 ohms.
Step 5: Conclusion
The resistance of the thinner wire is 30 ohms, while the resistance of the thicker wire is 10 ohms. The ratio of their resistances is 3:1, which matches the ratio of their cross-sectional areas. This demonstrates the relationship between resistance, cross-sectional area, and length.
Two wires of same metal an have a same length but there are cross sect...
30 ohm
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.