# Relationship between radius drift speed and current

### Current and Drift Velocity

(3) Drift Velocity. Metallic conductors have large numbers of elctrons free to move btcmu.info elctrons which are free to move are called conduction electrons. But we have to be careful to keep the current constant. Suppose the radius four times so the drift velocity should decreases by a factor of 1/4. Let l is the length of the conductor and A uniforms area of cross-section. Therefore, the volume of the conductor = Al. If n is the number of free.

We begin by introducing a limited analogy using mass and gravitational field as limited analogues of charge and electric field. Alternatively, go straight to the electrical case. How much rain falls in a bucket per second? The top of a bucket has area A. Raindrops of mass m are falling at a constant speed v their terminal velocity.

Let's look at the cylinder length L, area A above the bucket in the diagram at right. The weight pulls them down, and air resistance or drag acts in the upwards direction. If they start from rest, there would be no drag, and their weight would accelerate them downwards until they reached their terminal velocity v.

## What is the relationship between drift velocity and wire cross sectional area please?

For sufficiently small droplets, the drag force would be proportional to their speed and we'll conveniently limit discussion to this case. The drag force also depends upon their radius, and on the viscosity of the air, but for raindrops of fixed size, let's include these effects in a constant of proportionality Kdrag.

We use this to substitute for v in equation 1 and get: Kdrag is only constant if the size is unchanged, so this proportionality refers to changing the mass by changing the density of the material from which the drops are made.

Let's now derive Ohm's law for gravity and raindrops. We'll need the gravitational potential Vgrav, which is the gravitational potential energy per unit mass, exactly analogous to the electrical case.

In the diagram, the cylinder is our resistor its air is resisting the motion of raindrops. So, to get the gravitational version of Ohm's law: In terms of the analogy, this mix is analogous to a particular substance that conducts electricity.

### Drift velocity and relation between drift velocity and electric current

Now let's think about this particular cylinder, with its given length and cross section analogous to a particular piece of wire.

More specifically electric current is the rate of flow of charge i.

The unit of current is the Ampere A and 1 Amp is therefore 1 Coulomb of charge passing each second. A current is caused by a voltage source making the electrons or charge carriers physically move around a circuit and so the flow of current is a dynamic process. Imagine a classic analogy, that of water moving through a pipe, the electrons in a wire are analogous to the water particles in a pipe because they move from one place to another.

- Drift velocity

The charge carriers are attracted to the positive side of the battery or whatever power supply is making them move and repelled from the negative side. The forces that cause a current are simple electrostatic forces. We shall see later that the charge carriers themselves move really very slowly and there are an awful lot of them in a good conductor however the 'knock on' effect is very fast, when one is made to move it bumps into its neighbour making that one move etc etc.

The electrical effects that we observe, such as lights coming on immediately the switch is closed, are due to this 'knock on' effect and this explains the observation that a complete circuit is needed for current flow because if one charge carrier cannot cross a gap in the circuit all the other charge carriers behind cannot move either and current does not flow anywhere in the circuit. It is usual to use the term charge carriers to describe the particle that physically move when a current flows.

In metals these charge carriers are electrons, in semi-conductors they may be electrons or 'holes', in an ionic solution both positive and negative ions move and in a gas both electrons and ionised gas particles move.

Drift velocity and the transport equation Let us consider what is actually happening as a current flows through a material.

The charge carriers which are usually, but not always, electrons have a charge q and move through the material at a velocity v.

## RELATION BETWEEN CURRENT AND DRIFT VELOCITY

This velocity is called the drift velocity. Within the material not all the charged particles are free to move, the carrier density n is the number of charge carriers free to move per cubic meter. Calculate the drift velocity in a piece of wire where the current is 1 A, the free electron density is 5 x m-3 and the diameter of the wire is 1mm.