Electrical Quantities

These are the physical quantities associated with electricity:

• Charge, $Q$
• Current, $I$
• Voltage, $V$
• Power, $P$
• Energy, $E$

The cause of current flow

In order for a current to be present, electrons or other charge carriers must be moving. This movement is achieved by what is called an electromotive force (emf). An electromotive force is the difference in electric potential which causes charge to move. It is the energy ($E$) supplied per unit charge ($Q$) flowing from the source and is represented by $V$: $$ \begin{equation}\begin{aligned} V=\frac{E}{Q}\\ \end{aligned}\end{equation} $$ This gives rise to the formula: $$ \begin{equation}\begin{aligned} E=QV\\ \end{aligned}\end{equation} $$

Recall the formula for charge: $Q=It$

Combining these two we get: $$ \begin{equation}\begin{aligned} E&=QV=(It)V\\ \therefore E&=VIt\\ \end{aligned}\end{equation} $$ The amount of energy $E$ produced by a power source over a time interval $t$ is thus the product of the voltage $V$(e.m.f.) supplied, the current $I$ flowing and the time interval for which these are provided. We know that energy is related to power: $$ \begin{equation}\begin{aligned} E&=\color{orange}P\color{black}t\\ E&=\color{orange}VI\color{black}t\\ \end{aligned}\end{equation} $$ Thus electrical power: $$ \begin{equation}\begin{aligned} P=VI\\ \end{aligned}\end{equation} $$

Mission details

1. Find the energy produced by a power source with charge $40\ C$ and voltage $5\ V$.
2. If the power produced by a source is $500\ W$, find the current flowing from the source if a voltage of $17\ V$ is detected across its ends.

Electric energy can be converted to and from other forms of energy. Some examples of energy conversion are:

• Electric energy into kinetic energy in an electric motor
• Kinetic energy into electric energy in a dynamo (generator): https://www.bbc.co.uk/bitesize/guides/zgb9hv4/revision/1
• Electric energy into heat energy in a heating coil
• Electric energy into light in a bulb
• In a hydroelectric dam, the potential energy of the water becomes kinetic energy and this kinetic energy is used to turn turbines which convert it into electric energy

Conservation of electrical energy

See the following link:

• https://greenliving.lovetoknow.com/why-is-it-important-conserve-electricity

Mission details

1. A power heater runs on $220\ V$ for a time of $4\ minutes$. If it sustains a current of $2\ A$ throughout this time interval, calculate the energy expended by the heater.
2. Find the power rating of a heating element if $20,000\ J$ of energy are produced in a time interval of $2\ minutes$. If the current is limited to $5\ A$, what is the voltage present?