## Electrical systems, part 1 – Ohms law

In this article, you can read about the basic properties of electrical voltage, current, and resistance and Ohm’s law which describes the mathematical relationship between the three quantities.

# Ohms law

The mathematical relationship between voltage (volts), resistance (ohms), and current (amperes) is described by a formula, Ohm’s law, which was formulated by a German physicist, Georg Ohm, in the early 19th century.

Ohm’s law determines the relationship between electrical properties

• Voltage (U) measured in the unit Volt (V)
• Resistance (R) measured in the unit Ohm (Ω)
• Current (I) measured in the Ampere (A) unit

The formula looks like this

U = R * I

If you remember a little from the math lessons in primary school, you may remember that you can change the formula so that you can calculate, for example, resistance if you know the voltage and current.

R = U/I

or if you want to calculate the current if you know voltage and resistance

I = U/R

If we assume that the current consumed by the connected consumer is 10A and the voltage 12V, then how much resistance (R) does it have?

We use the version of the formula that calculates resistance using voltage and current and if we insert measured values we get R = U / I = 12/10 = 1.2Ω

## Electrical power

In addition to all electrical equipment having information on what form of electricity it should be connected to, there is also information on what power they require or what power they have. For example, the effect on elements, lamps and electric motors is stated. The effect tells you how ”strong” the equipment is and you have to make sure you have an electrical system that can deliver this effect. How it affects the electrical system I will return to in a later article.

You can calculate what effect (P) a certain voltage and current corresponds to with a formula that is derived from Ohm’s law and that looks like this.

• Power (P) is measured in watts P = U * I

With this formula, you can also calculate how much current a certain component will draw when it is running. Then the formula becomes

I = P/U

In the picture below, a 5W lamp is connected to a battery with a voltage of 12V. How much power will the lamp require?

With the formula for electrical power P = U * I we know that I = P / U and if we insert 5W and 12V in the formula we come to the conclusion that I = 5/12 ≈ 0.4 A

### Electrical energy

There is another concept that is good to know and that is energy. Energy can be stored in many forms, eg as diesel, wind, flowing water, solar radiation, food, battery e.t.c.

In our case, we need energy to convert it into electricity that is distributed to the boat’s electrical consumers. We also need to be able to store energy because we can not always or do not want electricity production started. Storage takes place in the boat’s batteries or, if we have a power plant, in fuel for the power plant.

In the case of electrical energy, it is calculated using the formula

• Energy is denoted E and has the unit Joule (J) or watt-second (Ws).
• Power is denoted P and has the unit watt • The time that the power is consumed denoted t and has the unit second (s)

E = P * t

## Unit conversion energy

Watts seconds can be converted to Wh or kWh which is an energy measure that is often used to indicate energy consumption in the home.

To convert Ws to unit Wh, you only need to know that it takes 3,600 seconds in one hour, which means that

1 Wh = 3 600 Ws which means that 1 Ws = 1/3 600 Wh

To convert Wh to kWh, you need to know that there is 1 000 Wh at 1 kWh, which means that

1kWh = 1 000 Wh which means that 1 Wh = 1/1 000 kWh

## Amount of energy in a 100Ah car battery

When storing electricity in batteries, they have a label on how much energy they contain (what capacity they have) when they are fully charged. This measure is ampere-hours (Ah) and tells how long the battery can supply power before it is completely discharged. A 12V car battery that has a capacity of 100Ah, can keep a 12V lamp that draws 1A lit for 100 hours.

#### How much Joule energy is in a battery like this?

Let’s use the power formula and the energy formula to calculate this.

The lamp is 12V and draws 1A and can be lit for 100 hours. First, we have to calculate the power, P = U * I where we insert 12V and 1A and get P = 12 * 1 = 12W.

Then we convert 100 hours to seconds and get 100 * 3,600 = 360 000 seconds

Voila, according to the formula E = P * t, the energy in a 100Ah car battery is approximately 12 * 360 000 = 4 320 000 J, ie just over 4 million Joules.

#### Hmm, how much is 4 million Joules?

From the section on energy, we remember that 1J = 1Ws and Ws we can convert to Wh (it takes 3,600 seconds in one hour). Then it is easy to convert Wh to kWh which we are more used to handling from the electricity bill at home.

First, we convert Ws to Wh with the formula above that gives that

4 320 000 Ws = 4 320 000 * 1/3600 Wh = 1 200 Wh

Then we convert 1,200 Wh to kWh

1 200 Wh = 1 200/1 000 kWh = 1.2 kWh

## Finally

By calculating how much power the equipment consumes when it is running, you can calculate how much energy needs to be supplied on average each day. You will also be able to calculate the cable area and the size of the fuses.

Once you know the energy consumption, you can calculate how much battery bank and charging capacity are needed to keep the equipment running.