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The Two Most Useful Equations in Electronics

by Chris - June 25th, 2011.
Filed under: Solar Education. Tagged as: , , , , .

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This post expands upon the Basic Electrical Concepts post.

There are two important equations that are used in every electrical project. A person can usually debug an electrical circuit using only these two equations, so long as they are good with logic or algebra. However, before we can discuss them, we need to cover two more definitions.

Electrical Energy

Energy is measured in units of joules. Energy is a way of measuring work, and is abbreviated in equations as ‘W’. Like charge, energy is not dependent on time, and also like charge, it is rarely measured directly.

Power

Power is the use of energy with respect to time. It is much more practical to measure power than energy directly because time is always moving. Power is abbreviated as ‘P’ in mathematical equations and is measured in units of watts. In equation form, the relationship of power to energy is written like this:

$P = W/t$

Stated as power is equal to joules per second.

Horsepower is also a measure of power. Specifically, 1 horsepower is equal to 746 watts:

$1 HP = 746 watts$

Ohm’s Law

The first equation, which is hands down the most important equation in electronics, is Ohm’s Law. It is mathematically expressed as:

$V = I * R$

In english, this would be stated as voltage equals current times resistance. Voltage here is measured in volts (V), current in amps (I), and resistance in Ohms (Ω).

Ohm’s Law is so powerful because it governs all electric circuits. If you know two of the above variables – in any circuit – you can figure out the third. Consequently, you can arrange the equation to solar for current or resistance:

$I = V/R$
$R=V/I$

The Power Equation

Everything comes back to power. Think about it. Your engine puts out a certain amount of horsepower, an electric motor puts out certain amount of watts, your lights are have a certain wattage rating; so does your electric heater. Power is the tangible product of electrical energy in motion. For this reason, the power equation is arguably the second most important equation in electronics:

$P=V*I$

Stated in english: power equals voltage times current. It can also be rearranged to solve for the other variables:
$V=P/I$

$I=P/V$

One of the most practical uses of this equation is to measure the current draw of a device. Here is an example: This Rule Marine Bilge Pump draws 2.1 amps:

How much power does it use?

Using our equation, 12 volts times 2.1 amps equals 25.2 watts!

$12 * 2.1 = 25.2$

Let’s say we didn’t know the current draw but we were able to read the power rating of 25 watts off the box instead. We can determine the current draw because 25 watts divided by 12 volts equals 2.1 amps (approximately):

$25/12 = 2.1$

Now, if we wanted to build a solar pond pump with this pump, we know our solar panels would have to generate 25 watts (or 2.1 amps at 12 volts) in order to power our system! That’s pretty useful information!