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# Drift Velocity Derivation

Drift velocity is defined as the average velocity attained by the particles (electrons) of a given material due to an electric field that is proportional to current. Ohm’s law can be expressed in terms of drift velocity as follows:

u=μE

Where,

u: drift velocity (m/s)

μ: material’s electron mobility (m2/V.s)

E: electric field (V/m)

## Derivation of Drift velocity

Following is the derivation of drift velocity:

$$\begin{array}{l}F=-\mu E\end{array}$$
$$\begin{array}{l}a=\frac{F}{m}=\frac{-\mu E}{m}\end{array}$$
$$\begin{array}{l}u=v+at\end{array}$$

Here,

v = 0

t = T (relaxation time that is the time required by an electron to return to its initial equilibrium value)

$$\begin{array}{l}u=aT\end{array}$$
(substituting for v and u)

$$\begin{array}{l}∴ u=(\frac{-\mu E}{m})T\end{array}$$
(substituting for a)

This is the final equation explaining drift velocity.

But as the temperature increases, the drift velocity of electrons increases in a metallic conductor.

See the video below to learn about the current electricity, drift velocity, and mobility.

This was the derivation of drift velocity. Stay tuned with BYJU’S and learn various other Physics topics.

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## Frequently Asked Questions – FAQs

### What is Ohm’s law?

Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperatures remain constant.

### What are the applications of Ohm’s law?

The main applications of Ohm’s law are:
• To determine the voltage, resistance or current of an electric circuit.
• Ohm’s law maintains the desired voltage drop across the electronic components.
• Ohm’s law is also used in DC ammeter and other DC shunts to divert the current.

### Define electric current.

Electric Current is the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.

### What are the advantages of AC over DC?

Following are the advantages of alternating current over direct current:
• AC is less expensive and easy to generate than DC.
• The distance covered by AC is more than that of the DC.
• The power loss during transmission in AC is less when compared to the DC

### What is watt less current?

Watt less current is defined as the current in an AC circuit when the average power consumption is zero.
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