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#### Notes by Category University Engineering

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# Charge & Current

Current is the rate of flow of charge. Charge is a physical property. The unit of charge is a Coulomb, C â€“ the amount of charge that passes in 1 second when the current is 1 ampere:

Q = It charge = current Ã— time

The charge on an electron is the smallest possible charge, and is known as the elementary charge, âˆ’e, where

e = 1.60Eâˆ’19
• (E notation is used on EngineeringNotes - it is a web-friendly way of writing standard form, as exponents are not always compatible with different devices and browsers. 1.60E-19 is the same as 1.60 x10^-19. Don't confuse it with E for energy or the fundamental charge, e)

A proton has the same charge, but positive, (+e).

Because e is the smallest value Q can take, any charge value must be a multiple of e - therefore we say that charge is quantised.

In most instances, charge is transferred via electrons - however there are a number of different so called 'Charge Carriers' depending on the material and state:

• In metals, the charge carriers are free, delocalised electrons (meaning they can move inside the material).

• Fluids, such as electrolytes, conduct with the use of ions.

• Gasses are insulators, but when enough voltage is applied electrons are torn out of atoms resulting in sparks â€“ this is called ionisation.

The magnitude of the current is dependent on number and speed of charge carriers. For example, a wire will have a larger current if there are more electrons flowing through it, or if there are the same number moving faster.

### Conventional Current

Conventional current suggests that charge moves from positive to negative (high potential to low potential), however electrons move the opposite direction due to their positive attraction.

## Kirchhoff's Laws

Being a fundamental physical property, charge must be conserved. It cannot be created nor destroyed - the total amount of electrical charge in the universe always remains the same.

### Kirchhoff's 1st Law

Since charge is conserved in a circuit, none can be lost at path junctions. The rate of flow of this charge is also unchanged, meaning the total current going into a branch equals the total current coming out of the branch, regardless of how many points are on the branch.

Current/charge is conserved around a circuit â€“ when the current reaches a branch it splits so that the total current in the branches is equal to the current before splitting.

### Kirchhoff's 2nd Law

This law applies the principle of conservation of energy to electrical circuits. It says that the amount of energy being put into the circuit (the E.M.F.) must equal the amount of energy coming out of the circuit (the P.D.):

Electrical energy is conserved in a circuit - the sum of the e.m.f.s around any closed loop equals the sum of the p.d.s around the closed loop.Â

Practically, these laws mean that in series, the voltage across all components adds up to the supply voltage and the current is the same across each component, while in parallel, the total voltage in each branch is the same and the current in the branches add up to the pre-branching current.

## Mean Drift Velocity

Mean drift velocity is the average velocity of charge carriers in a conductor. While the effect of electricity travels at the speed of light, the carriers (such as the electrons) actually move very slowly in a domino effect.

It is called â€˜drift velocityâ€™ because electrons do not all move in exactly the same direction, but randomly in all directions â€“ it's just that if you were to take an average of all their directions, this would tend towards one direction.

The current is dependent on the mean drift velocity, as shown in the current continuity equation:

I = Anev current = cross sectional area Ã— number density Ã— elementary charge Ã— velocity

The number density of electrons per metre cubed gives rise to different levels of conductivity for different materials.Â It is a fixed property of a material.

• Conductors (such as metals) have a huge number of free electrons per unit volume, and so the drift velocity is small even for high currents.Â

• Semiconductors (such as silicon) have fewer charge carriers, so the drift needs to be greater to achieve the same current.

• Insulators have very few, if not 0 charge carriers. This means whatever you put in the formula; the current is always 0.Â

This equation means that cross-sectional area has a vast effect on current. In order to maintain the same current in a narrower wire, a far higher drift velocity is required.

• The mean drift velocity is inversely proportional to the cross-sectional area

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