Physics, Electricity, 13-14

Electricity 1

Electrical Power and Energy

\begin{equation} \text{Power}=\frac{\text{Energy Transferred}}{\text{Time}}\nonumber \\ \end{equation}

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.

\begin{equation} Q=It\nonumber \\ \end{equation}

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

\begin{equation} V=\frac{W}{Q},\nonumber \\ \end{equation}

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

\begin{equation} V=IR\nonumber \\ \end{equation}

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.