What will the resistance be in a replacement wire that is twice the length and one half the cross-sectional area of the original wire?

As the length of wire gets doubled, the cross-sectional area will become half of its previous value because volume of wire remains constant. Hence, we can see that the new resistance is four times the previous resistance.

How do you calculate resistance in a wire?

Use the results to calculate the resistance of each length of wire by using R = V/I, where R is resistance, V is voltage and I is current.

Does a wire twice as long have twice the resistance?

As a wire gets longer its resistance increases, and as it gets thinner its resistance also increases because its cross sectional area decreases. Doubling the length will double the resistance, but the wire also must get thinner as it is stretched, because it will contain the same amount of metal in twice the length.

What is resistance of a wire?

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor. The resistance of a conductor, or circuit element, generally increases with increasing temperature.

What do VI and R stand for in Ohm’s law?

resistance
where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms.

How do you find the resistance of a material?

The resistance of a cylindrical segment of a conductor is equal to the resistivity of the material times the length divided by the area: R≡VI=ρLA. The unit of resistance is the ohm, Ω. For a given voltage, the higher the resistance, the lower the current.

Which wire has twice the resistance of the other wire?

The other wire will have twice the resistance of the first wire. This is true because resistance varies directly with length; 1/2 length with give 1/2 the resistance. Also resistance varies inversely as the square of the diameter since it varies as the direct inverse of the area.

What happens when the diameter of a wire is doubled?

Thus when the diameter of a wire is doubled (made 2 times), its resistance becomes one-fourth (1/4), and if the diameter of a wire is halved (made 1/2), then its resistance becomes four times (4 times).

How is the resistance of a material related to its diameter?

So it’s proportional to the square of diameter. Resistance is inversely proportional to cross sectional area. So if the diameter is halved the cross-sectional area is quartered and the resistance is quadrupled. Share Cite Follow edited Nov 24 ’17 at 22:06

What is the relationship between cross sectional area and resistance?

\\$\\begingroup\\$ Cross sectional area is the area of the end of the wire (assuming a perfectly flat right angle cut). So it’s proportional to the square of diameter. Resistance is inversely proportional to cross sectional area. So if the diameter is halved the cross-sectional area is quartered and the resistance is quadrupled.