a wire has a resistance of 10 ohms. The length of the wire is doubled, and its radius is also doubled. What is the new resistance?
Resistance is proportional to length and inversely proportional to cross section, so the resistance becomes 5 Ohm.
is there math to show how you got that
To find the new resistance of the wire, we need to consider the relationship between resistance, length, and radius of a wire.
1. Resistance is directly proportional to the length of the wire. This means that as the length of the wire doubles, the resistance will also double.
2. Resistance is inversely proportional to the cross-sectional area of the wire. The cross-sectional area is determined by the radius of the wire. So if the radius is doubled, the cross-sectional area will increase by a factor of 4 (since the area of a circle is πr^2).
Now, let's calculate the new resistance:
Given:
Original resistance (R1) = 10 ohms
Original length (L1) = Original radius (r1) = 1 (unit)
New length (L2) = 2L1 = 2 units
New radius (r2) = 2r1 = 2 units
To find the new resistance (R2), we can use the following formula:
R2 = R1 * (L2 / L1) * (r1 / r2)
Substituting the given values:
R2 = 10 ohms * (2 / 1) * (1 / 2)
R2 = 10 ohms * 2 * 0.5
R2 = 10 ohms * 1
R2 = 10 ohms
Therefore, the new resistance of the wire is also 10 ohms.