a wire has a resistance of 6 ohm it is stretched out to a new length which is three times its original length what is the resistance of the longer wire?assume uniform diameter.resistivity and density are constant
R = rho l/A
l is now three times as big. What's the new resistance?
A wire of resistance20ohm is stretched to 3times it's original length calculate it's new resistance
To find the resistance of the longer wire, we need to consider the relationship between resistance, length, and cross-sectional area.
The resistance of a wire is given by the formula:
R = (ρ * L) / A
Where:
R = Resistance
ρ = Resistivity of the material
L = Length of the wire
A = Cross-sectional area of the wire
In this case, the resistivity and diameter of the wire are assumed to be constant, so ρ and A will remain the same.
Let's break down the problem step by step:
1. Given that the resistance of the wire (R1) is 6 ohms, we can write:
R1 = (ρ * L1) / A
2. Now, let's consider the longer wire, which is stretched to three times its original length. The new length is L2 = 3 * L1.
3. To find the resistance of the longer wire (R2), we can substitute L2 in the formula:
R2 = (ρ * L2) / A
4. Since we are assuming constant resistivity and diameter, we can rearrange the equation:
R2 = (ρ * (3 * L1)) / A
= 3 * ((ρ * L1) / A)
= 3 * R1
Therefore, the resistance of the longer wire (R2) is three times the resistance of the original wire (R1). In this case, R2 = 3 * 6 ohms = 18 ohms.