Basics of Electricity

Basics of electricity: what is the potential difference?

This definition is equivalent to a difference in electric potential between two spatial points (indicated by its name). The way to achieve this difference of electric potential is usually through starting chemical reactions (which move electrons that generate a potential difference), moving magnets, water-powered turbines, etc.

The voltage difference will create a direction for the charges to flow. The voltage can be described mathematically as

\[V = \frac{W}{Q}\]

In this equation, V is the potential difference in volts (V), W is the energy in joules (J), and Q is the charge in coulombs (C). The device used to measure potential difference or voltage is a voltmeter.

Basics of electricity: what is resistance?

The lower the resistance of a component, the higher the current flows through the component. Materials with lower resistance make better conductors (so the lower the resistance of a particular material, the better it is as a conductor). That’s why most wires are made up of copper because this material has a low resistance value. We can calculate the resistance thanks to Ohm’s law, which defines resistance as the ratio of the potential difference and the current:

\[R = \frac{V}{I}\]

R is the resistance measured in Ohms (Ω), V is the potential difference measured in volts (V), and I is the current measured in amperes (A).

Basics of electricity: what is electric power?

Since electric circuits with a current involve the movement of charges, there is an associated power (energy per unit of time) that can be calculated in the quantities we have already studied. The expression for the electric power is the following:

\[P = I \cdot V = I^2 \cdot R = \frac{V^2}{R}\]

In this equation, the power P is measured in watts (W), and we have used Ohm’s law several times to obtain the power in terms of two of the three basic quantities.

Basic components of electric circuits

The basic electrical systems where we care about voltage, current, and resistance are electric circuits. They are structures made out of electric devices, such as cables, resistors, switches, power sources, etc., where the potential difference is established and a current is formed. The setup determines the specific characteristics of each circuit and its possible applications.

Basic knowledge of circuits

We can describe circuits by using diagrams with standard symbols that indicate the role of each component in the circuit. The main components are:

• Sources, which supply voltage and/or current.
• Wires that transport the current.
• Resistors, which offer resistance to the flow of current.

The majority of other complex devices are usually described in terms of their resistance and extra conditions. For instance, a lightbulb is a resistor that shines when a current flows through it. Below is an example of a basic circuit (don't worry about the cix symbol).

Resistance association

The laws that resistors obey when there is more than one in a circuit are important because they allow us to simplify circuits or achieve certain effects. The two main forms of association of resistors we use are resistances in series and resistances in parallel.

• Resistances in series: n resistors are on the same wire or conductor one after another, and the wire does not bifurcate (divide into branches). The resulting resistance of the set of resistors is the sum of their individual resistances:

\[R_{Total} = \sum_i R_i\]

• Resistances in parallel: n resistors are on different branches that originated from a division of the same wire. The following equation gives the resulting resistance of the set of resistors.

\[R_{Total} = \frac{1}{\sum_i \frac{1}{R_i}}\]

Kirchhoff’s Laws

Finally, when considering circuits, we have to take into account two laws of conservation that are named after the scientist Gustav Kirchhoff:

• Conservation of current: whenever we reach a node of wires/conductors, the current entering the node must equal the current leaving it (conservation of charge and, hence, current).
• Conservation of voltage: whenever we consider a closed circuit or a closed loop in a circuit, the sum of the voltage supplied by all batteries must equal the drop of potential caused by every element in the closed-loop. This is simply Ohm’s law applied to closed circuits.