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A current (I) flows through a uniform wire of diameter (d) when the mean drift velocity is V. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron is
  • a)
    V/4
  • b)
    V/2
  • c)
    4V
  • d)
    2V
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A current (I) flows through a uniform wire of diameter (d) when the me...
I = neAvd

so, drift velocity will be

vd = I / neA

here

A = πr2

so,

vd = I / nerπ2

now,

if the radius is doubled

vd' = I /  neπr'2 =  I /  neπ(2r)2

thus, we get

vd' = (1/4).(I / nerπ2)

or

vd' = vd/4
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Community Answer
A current (I) flows through a uniform wire of diameter (d) when the me...
Explanation:

The current through a wire is given by:

I = nAev

where n is the number density of free electrons, A is the cross-sectional area of the wire, e is the charge of an electron, and v is the drift velocity of the electrons.

Since the wire is uniform, the number density of free electrons and the charge of an electron are constant. Therefore, we can write:

I ∝ A v

1. Current through a wire of diameter d:

Let the current through a wire of diameter d be I1. Then, we can write:

I1 = nπd²/4 ev

2. Current through a wire of diameter d/2:

Let the current through a wire of diameter d/2 be I2. The cross-sectional area of the wire is π(d/2)²/4 = πd²/16. Therefore, we can write:

I2 = nπd²/16 e(V2)

where V2 is the drift velocity of the electrons in the wire of diameter d/2.

3. Equating the currents:

Since the same current flows through both wires, we can equate I1 and I2:

I1 = I2

nπd²/4 ev = nπd²/16 e(V2)

Canceling out the common factors, we get:

V2 = 4V

Therefore, the mean drift velocity of electrons in the wire of diameter d/2 is 4 times the mean drift velocity of electrons in the wire of diameter d.
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A current (I) flows through a uniform wire of diameter (d) when the mean drift velocity is V. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron isa)V/4b)V/2c)4Vd)2VCorrect answer is option 'C'. Can you explain this answer?
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A current (I) flows through a uniform wire of diameter (d) when the mean drift velocity is V. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron isa)V/4b)V/2c)4Vd)2VCorrect answer is option 'C'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A current (I) flows through a uniform wire of diameter (d) when the mean drift velocity is V. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron isa)V/4b)V/2c)4Vd)2VCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A current (I) flows through a uniform wire of diameter (d) when the mean drift velocity is V. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron isa)V/4b)V/2c)4Vd)2VCorrect answer is option 'C'. Can you explain this answer?.
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