4.3.1 Battery Life

Batteries are electrochemical devices created by embedding two different metallic plates into a third one. This third one, the electrolyte, is responsible, broadly speaking, for creating a chemical reaction in such a way that one of the elements ends with excess of electrons (negative charges) and the other one with an excess of positive charges – in other words, to create an imbalance of charges between the plates.

To summarize how chemical energy is converted into electrical energy, let us take an example of a typical car battery: one plate of pure lead and another one made of lead dioxide both immersed in a solution of sulfuric acid diluted with water. Chemical reaction causes the lead to become negatively charged and the lead dioxide to become positively charged.

The element with excess of electrons will be the negative pole (cathode) and the other element will be the positive pole (anode).

This difference in the number of electrons between the poles is called “difference in electric potential” or popularly, “voltage.”

Any element, like a light bulb, for example, connected between the poles, will provide a path for the excess of electrons of the lead element to migrate to the lead dioxide, which lacks electrons. As the reaction happens, most of the sulfuric acid in the electrolyte is consumed and used to convert both plates into lead sulfate, and the electrolyte turns into, mostly, regular water.

At some point, all three elements are electrically balanced, current stops flowing, and the battery dies.

The process of charging the battery will apply energy to the plates and electrolyte to reverse the reaction, making the plates to be lead dioxide and lead and the electrolyte sulfuric acid and water, again.

4.3.2 Batteries in Series

Consider two identical batteries connected in series, like shown in Figure 4.1. The positive pole of one battery is connected to the negative of the other and two wires are connected to points A and B.

If each battery has a voltage of 1.5 V, two batteries connected in series will provide a combined voltage of 3 V. This will be the value measured across A and B.

Batteries can only provide a limited amount of current. If each battery on the given example can provide 0.2 A of current, connecting any number of batteries in series will not change that.

Conclusions:

• Two power supplies in series will have their voltages added.
• Two power supplies in series will not have their currents added.

4.3.3 Batteries in Parallel

Figure 4.2 shows two identical batteries connected in parallel. The positive poles and negative poles are connected together.

Supposing each battery can provide 1.5 V and 0.2 A,¹ the voltage across AB will be 1.5 V, and together the batteries will be able to provide 0.4 A of current, which is the sum of their individual currents.

Conclusions:

• Two power supplies in parallel have their currents added.
• Two power supplies in parallel will not have their voltages added.

4.4.1 Never Invert Polarities

Inverting a battery in a block of batteries in series, like shown in Figure 4.3, or in parallel may represent a danger situation.

The other batteries will force current circulation across the inverted one, generating excessive heat that may lead to fire hazard and explosions.

4.4.2 Never Use Different Batteries

A battery is only capable of providing a limited amount of current and voltage.

If you connect batteries with different current capabilities in series, for example, 2, 4, and 6 A, the largest battery will force 6 A of current through batteries that cannot handle that amount of current. Excessive heat may be generated, again creating a danger situation.

The same is true for batteries with different voltages in parallel.

4.4.3 Short‐Circuiting Batteries

Never short‐circuit a battery like shown in Figure 4.4. Current will flow between them, at maximum level, making both batteries explode and catch fire.

4.5.1 DC Characteristics

• Current and voltage are constant over time.
• They are generated by chemistry and are very difficult to deploy in large scale.
• They never change polarity over time.
• Current only flows in one direction during all time.
• A DC voltage is not able to cross large distances. They lose power, considerably, if transmitted over long distances.

4.6.1 Mountains

To understand why, consider two mountains like shown in Figure 4.6 and a path that one can climb from A to C, including a point B in the middle.

A person standing on point A can climb to C in two phases: from A to B, resting at B a little bit, and then from B to C.

In terms of physics, the climber is going against gravity and, by doing so, accumulates gravitational potential energy.

Gravitation potential energy is calculated by the following formula.

If point A is at sea level, B is at 100 m, C is at 200 m, and a person weights 70 kg, we can use the given formula and calculate that the person will gain a potential energy of 68.6 kJ by climbing from A to B and the same amount, again, by climbing from B to C.

If we choose point A as zero reference, we conclude that the person will have a potential energy of zero at point A, 68.6 kJ at B, and 137.2 kJ at C.

What happens if instead of point A we select point B as zero reference?

If we do, we conclude that point C is 68.6 kJ over B and A is 68.6 kJ under B. In other words, in relation to B, the energy at C is 68.6 kJ and the energy at A is −68.6 kJ.

The negative sign is used to indicate that the potential level of A is below the reference point.

Now consider two batteries in series, like shown before, but, this time, we take them apart to include a third point B, like shown in Figure 4.7.

Figure 4.7 shows three points: A, B, and C. No need to remember the mountain analogy.

If each battery can provide a voltage of 1.5 V and we use point A as zero reference, we see that point B will be 1.5 V and point C will be 3 V above A.

On the other hand, if we use point B as a zero reference, C will be at 1.5 V above B and A will be −1.5 V below B. Again, the negative sign is used to show that A is below B.

This example shows the concept of negative electric potentials that are nothing more than a way to tell if a voltage is above or below a zero reference. This zero‐reference point is called ground point, or simply ground, or in some cases, earth point.

4.8.1 AC Characteristics

• Can be easily created in large or small scale with electric generators.
• The levels of voltage and current vary cyclically with time.
• Voltage polarity may change with time.
• Current direction changes with time.
• Can travel large distances over wires with minimum losses.

4.8.2 AC Cycles

Figure 4.10 shows a graph representing an alternating voltage.

In Figure 4.11, we can see that alternating waves have a positive cycle and a negative cycle and vary over time in intensity.

The wave starts at 0 V, increases until it reaches V⁺, and then decreases to a negative level V⁻, repeating the whole pattern after that, ad infinitum.

Because the alternating voltage follows a cyclic pattern going up and down constantly, over time, it oscillates at a specific constant frequency. This frequency is measured in Hertz,³ meaning cycles per second,⁴ and is represented in the SI by the letters Hz.

4.8.3 Period and Frequency

Figure 4.12 shows that the alternating wave starts at 0 and goes up and down and after a period equal to T starts repeating it.

In the given example, T is equal to 4 s and is known as the wave’s period of oscillation.

The frequency and the period of a wave are related by the following formula.

4.8.4 Peak‐to‐Peak Voltage

Consider the wave shown in Figure 4.13, where voltages vary from 20 to −20 V. These values are measured against the 0 and are called peaks.

Remembering the mountain analogy, we can now use the negative peak as zero reference. If so, we can say that the positive peak is 40 V above that. In other words, 40 V is the difference between both peaks, also known as peak‐to‐peak voltage.

4.8.5 DC Offset

We have described DC and AC as two separate entities, but we never said that they cannot exist together.

Observe the alternating voltage shown in Figure 4.14. The wave reference rests, vertically, at 0 V. The wave varies from 20 to −20 V.

Now suppose we add 10 V continuous to that wave. The result is seen in Figure 4.15.

By observing Figure 4.15, it is clear that the wave shifted up by 10 V. Now, its positive peak is at 30 V and its negative peak is at −10 V. The wave now rests, vertically, at 10 V and not at 0 V as before. We say, in that case, that an offset of 10 V was applied to the alternating voltage.

If the offset is negative, −10 V, for example, the wave of Figure 4.14 will shift down and be like the one shown in Figure 4.16. The wave now rests at −10 V and variates up and down to 10 V and −30 V, respectively. In other words, we pushed the wave down by 10 V.