# Physics, Electricity, 13-14

## Electricity 1

### Electrical Power and Energy

$$\text{Power}=\frac{\text{Energy Transferred}}{\text{Time}}\nonumber \\$$

Power is measured in watts, and energy in joules. Alternatively, one kilowatt-hour is the energy transferred in one hour from a source of power 1000W; 3.6MJ.

### Electric Current

#### Charge

Current is a flow of charge. Charge itself is a fundamental property of matter. Charge can be positive or negative, and opposite charges attract. Charge itself is measured in coulombs, with the charge on one electron being $$-1.6\times 10^{-19}$$C.

#### Conductors and Insulators

Conduction is the flow of electric charges through a material. An insulator is a material that will not readily conduct electricity, as it has no free charges - the tightly bound electrons would require a relatively large amount of energy to be freed.

By rubbing together two insulators, electrons are transferred from one material to another, leaving neither material with a neutral charge.

Metals are good conductors due to the fact that some of their atomic electrons are free to move between atoms and carry charge.

#### Current

Electrostatic phenomena are when there is no flow of continuous charge. A continuous charge is known as a current.

$$Q=It\nonumber \\$$

The direction of conventional current is from positive to negative. However electrons, being negatively charged, flow from negative to positive.

Current is the rate of flow of charge: With a current of one ampere, one coulomb will pass a given point every second.

#### Electric Circuits

An electric current will be set up in a conductor if there is:

• An energy source, such as a battery made up of cells

• A continuous circuit

#### Conservation of Charge

Charge is conserved wiothin a circuit. At any given point, the input and output charge must be equal - Kirchoff’s First Law

In a series circuit, current is the same everywhere. In a parallel circuit, the sum of the current in branches is equal to the total current.

## Potential Difference

The amount of energy transferred when a charge moves between points is known as the potential difference (pd), with the term voltage normally being used. This is analogous to gravitational potential difference - a larger potential difference increases the energy that is transferred by a charge moving through it.
The potential difference between two points is defined as the work done per unit charge passing between those two points

$$V=\frac{W}{Q},\nonumber \\$$

where $$W$$ is work done. Potential difference is measured using a voltmeter connected in parallel (Ammeters are connected in series). Voltmeters are assumed to have infinite resistance, and ammeters to have no resistance.

### Conservation of energy in a circuit

The total energy transferred by the charge must be equal to the energy it receives from the battery. The energy transferred from a battery/source is known as the electromotive force (emf).

The sum of the potential differences around a circuit is equal to the sum of the electromotive forces - Kirchoff’s Second Law

Potential differences across a series circuit will sum to the EMF, whereas potential differences across parallel components are equal.

### Power, Potential Difference, and Current

\begin{gather*} P=\frac{W}{t} \\ V=\frac{W}{Q} \\ P=\frac{QV}{t}=IV \\ E=VIt \\ \end{gather*}

## Resistance

• Metals are the most common conductors

• Free electrons move randomly between fixed positive ions

• If a potential difference is applied, the electrons will accelerate towards the positive connection

• They then collide with the positive ions, and lose kinetic energy, which is transferred to vibrational energy in the ionic lattice

### Resistance and Ohm’s Law

$$V=IR\nonumber \\$$

Ohm’s Law: Provided that temperature and other physical conditions remain constant, the current through an ohmic conductor is proportional to the potential difference across the conductor.