A potential difference V is applied across a conductor of length ‘l’. How is the drift velocity affected when V is doubled and l is halved?

The formula for drift velocity is given as,

|vd| = eτ/mxE

However, we know that E = V/l

where V refers to the potential difference

l is the length of conductor.

Substituting this value of E in the drift velocity formula, we have:

|vd| = eτ/m(Vl)

Therefore, the drift velocity is proportional to the potential difference applied across the conductor.
The length of the conducting wire is inversely proportional to drift velocity. V becomes 2V when the potential difference applied across the conductor is doubled.
When the conductor’s length is half, l becomes l/2.

Putting these values in the drift velocity equation, we have:

|vd′|=eτ/m(4V/l)

On simplifying the equation further, we get:

|vd′|=4eτ/m(V/l)

We know that eτm(V/l)=|vd|

Substituting this in the above equation we get

|vd′|=4|vd|

Therefore, we can observe that when the potential difference of a conductor is doubled and the length of the conductor is half, the drift velocity increases by four times.

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In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

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A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

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A potential difference V is applied across a conductor of length ‘l’. How is the drift velocity affected when V is doubled and l is halved?

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3.A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.

4.In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

5.A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

6.The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

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Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.

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The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.