1) a wire of length 1m has a resistance of 2 ohm.obtain the resistance if specific resistance is double,diameter is double and the length is made three times of the first.
specific r double ---> double r
diameter doubles --> resistance 1/4
lenght * 3 ----> r *3
2/4*3 = 3/2
3/2 * 2 ohms = 3 ohms
Well, well, let's unravel this puzzle. So, we have a wire with a length of 1 meter and a resistance of 2 ohms. If I understand correctly, you want to know what happens to the resistance if the specific resistance of the wire doubles, the diameter doubles, and the length becomes three times the original length.
If the specific resistance of the wire doubles, that means the wire will be twice as resistant to the flow of electric current. So, the new resistance would be 2 ohms * 2 = 4 ohms.
Now, let's look at the changes in diameter and length. If the diameter doubles, it means the cross-sectional area of the wire increases by a factor of 4 (since area is proportional to the square of the diameter).
And if the length is made three times the original, it means we're dealing with a wire that's 1 * 3 = 3 meters long.
Now, here comes the fun part! The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
So, if the length is three times the initial length, the resistance would be three times the initial resistance (4 ohms * 3 = 12 ohms).
And if the cross-sectional area increases by a factor of 4, the resistance would decrease by a factor of 4.
Therefore, the final resistance would be 12 ohms / 4 = 3 ohms.
Ta-da! So, with all these changes, the resistance of the wire would be 3 ohms.
To find the resistance, we can use the formula:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
Let's break down the changes:
1. The specific resistance (ρ) is doubled.
2. The diameter is doubled, which means the radius is also doubled. Since diameter = 2 * radius, the radius becomes twice the original value.
3. The length is made three times the original length.
Let's solve this step by step:
1. The specific resistance (ρ) is doubled: This means we multiply the original resistance by 2.
Original resistance = 2 ohms
New specific resistance = 2 * 2 = 4 ohms
2. The diameter is doubled: This means the radius is doubled. If the original radius is 'r', the new radius will be 2 * r.
3. The length is made three times the original length.
Original length = 1m
New length = 3 * 1 = 3m
Now we need to calculate the new resistance using the updated values.
Step 1: Calculate the new cross-sectional area (A).
Since the diameter is doubled, the new radius is 2 * r.
The formula for the area of a circle is A = π * r^2.
Using the original radius as 'r', the new area would be:
Original area = π * r^2
New area = π * (2 * r)^2 = π * 4 * r^2
Step 2: Substitute the values into the resistance formula.
Using the new values of specific resistance (ρ), length (L), and area (A), we can calculate the new resistance (R).
New resistance = (ρ * L) / A = (4 ohms * 3m) / (π * 4 * r^2)
Simplifying the expression, we have:
New resistance = (12 ohms * m) / (4 * π * r^2)
Therefore, the new resistance is (12 ohms * m) / (4 * π * r^2).