Suppose a electrical circuit uses 18 gauge wire and the drift velocity of electron through it wasvd = 0.15mm/s . Now the wire has been replaced by a 12 gauge copper wire which has twice thediameter of 18-gauge wire. If the current remains the same, what effect would this have on themagnitude of the drift velocity vdi) none— vd would be unchanged;ii) vd would be twice as great;iii) vd would be four times greater;iv) vd would be half as great;v) vd would be one-fourth as great.
Question
Suppose a electrical circuit uses 18 gauge wire and the drift velocity of electron through it wasvd = 0.15mm/s . Now the wire has been replaced by a 12 gauge copper wire which has twice thediameter of 18-gauge wire. If the current remains the same, what effect would this have on themagnitude of the drift velocity vdi) none— vd would be unchanged;ii) vd would be twice as great;iii) vd would be four times greater;iv) vd would be half as great;v) vd would be one-fourth as great.
Solution
The drift velocity (vd) of electrons in a conductor is inversely proportional to the cross-sectional area (A) of the conductor. This relationship can be expressed as:
vd = I / (nAe)
where:
- I is the current,
- n is the number density of free electrons,
- A is the cross-sectional area of the conductor, and
- e is the charge of an electron.
Given that the current (I) remains the same, and the number density of free electrons (n) and the charge of an electron (e) are constants for a particular material (in this case, copper), we can see that the drift velocity is inversely proportional to the cross-sectional area of the conductor.
The cross-sectional area of a wire is proportional to the square of its diameter. Therefore, if the diameter of the wire is doubled (as in the case of replacing an 18-gauge wire with a 12-gauge wire), the cross-sectional area of the wire will be four times greater.
Since the drift velocity is inversely proportional to the cross-sectional area, if the cross-sectional area is four times greater, the drift velocity will be one-fourth as great.
So, the answer is (v) vd would be one-fourth as great.
Similar Questions
The drift velocity of electrons for a conductor connected in an electrical circuit is Vd. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be
here is a current of 20 amperes in a copper wire of square metre area of cross-section. If the number of free electrons per cubic metre is then the drift velocity is:
In the figure provided a wire consists of two segments made from the same material but with different cross sectional areas such that A2𝐴2 = 2 A1𝐴1. Which of the following is true about the strength of the electron drift velocities in the two segments? (vd)1(𝑣𝑑)1 = 2 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 4 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 0.5 (vd)2
An 18 gauge copper wire with a diameter of 1.02 mm carries a constant current of 1.65 A to a 200 W lamp. The free electron density in the wire is 8.5 X 1028 per cubic meter. Find (a) the current density and (b) the drift speed.
If the resistance of a wire doubled and the potential difference stayed the same, what would happen to the current?it would doubleit would halveit would stay the same
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.