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A current I flows through a uniform wire of diameter d when the mean electron 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)
    2v
  • d)
    4v
Correct 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 e...
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A current I flows through a uniform wire of diameter d when the mean e...
Brother, I may be wrong but I think the correct answer is (d). As:
i=n�a�e�v and I=n�e�A�V.
But we have i=I, then 
neav= neAV
>av=AV          but, a=π(d/2)square 
                              >a=π(d sq./4).       Similarly we have A=π (d sq./16)
Now putting the value of a and A in the eqn we get
>π(d sq./4)/π(d sq./16)=V/v
>4v=V
Hence,the new velocity is 4v.
               
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A current I flows through a uniform wire of diameter d when the mean e...
Explanation:

Formula: Current density J = nqVdA

Where,
n = Number density of electrons
q = Charge on an electron
Vd = Drift velocity of electrons
A = Area of cross-section of the wire

1. Let's assume the current flowing through the wire of diameter d is I.

2. The current density J is given by J = I / (πd²/4)

3. Using the formula for current density, we can write J = nqVdA

4. As the material of both wires is the same, the number density of electrons will also be the same. Hence, n is constant.

5. Since the current is the same in both wires, we can equate the current densities:

J₁ = J₂
I / (πd²/4) = I / (π(d/2)²/4)

6. Simplifying the above equation, we get:

d² = (d/2)² * 4
d² = d²
1 = 4

This is not possible, so there must be an error in our assumption.

7. Let's assume that the mean electron drift velocity in the wire of diameter d/2 is V₂.

8. Using the formula for current density, we can write J = nqVdA = nqV₂(d/2)²π/4

9. Since the current is the same as in the wire of diameter d, we can equate the current densities:

J₁ = J₂
I / (πd²/4) = nqV₂(d/2)²π/4

10. Simplifying the above equation, we get:

V₂ = 2V

11. Therefore, the mean electron drift velocity in the wire of diameter d/2 is 2V.

12. 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 2V. Hence, the correct answer is option C (2V).
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A current I flows through a uniform wire of diameter d when the mean electron 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)2vd)4vCorrect 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 electron 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)2vd)4vCorrect 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 electron 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)2vd)4vCorrect 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 electron 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)2vd)4vCorrect answer is option 'C'. Can you explain this answer?.
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