Electrotechnologic Systems / Ohms Law and Power

Ohms Law and Power

Current, Voltage and Resistance

An electrical circuit is a complete path for electrons to flow. This flow is what we call electric current, and it is measured in amperes (A), or amps.

Current flows when there is an electrical potential difference, or voltage, which is measured in volts (V). Voltage is the electromotive force that drives electrons around the circuit.

The flow of electrons through a circuit is impeded by resistance, which is measured in ohms (Ω). The relationship between voltage, current and resistance is defined by Ohm’s Law

Ohm's Law

The single most important relationship in electronics. Voltage (V), current (I) and resistance (R) are locked together:

$$ V = I \times R $$

Rearranged as needed:

$$ I = \frac{V}{R} \qquad R = \frac{V}{I} $$

Where $V$ is in volts (V), $I$ is in amperes (A) and $R$ is in ohms (Ω).

Watch Your Units

Milliamps (mA) are the natural unit for electronics that we tend to work with, but Ohm's law needs amps. Convert first!

$20\text{ mA} = 0.02\text{ A}$.

$4.7\text{ k}\Omega = 4700\ \Omega$

$1\text{ M}\Omega = 1\,000\,000\ \Omega$.

Mixing conversions is a very common source of wrong answers.

Worked Example — Ohm's Law

A 12 V supply is connected across a 470 Ω resistor. What current flows?

$$ I = \frac{V}{R} = \frac{12}{470} = 0.0255\text{ A} = 25.5\text{ mA} $$

Power

Power is the rate at which energy is transferred or converted — how fast electrical energy turns into heat, light, motion, etc. The formula we use for Power is:

$$P = {I} \times {V}$$

Ohm's Pie Chart

Between the Ohm's Triangle and the Power Triangle, you can solve for 6 of 12 potential equations.

Ohm's Law Triangle (V, I, R) Power Triangle (P, V, I)
$V = IR$ $P = VI$
$I = \frac{V}{R}$ $I = \frac{P}{V}$
$R = \frac{V}{I}$ $V = \frac{P}{I}$
These triangles will not help you solve everything.

Because $P$ and $R$ are unique to their triangles, it is initially impossible to use the triangle to solve for $I$ where you are given $P$ and $R$ - a question given in the 2022 exam.

Using Ohm's Pie Chart, you can solve for any unknown variable out of $P$, $V$, $I$, and $R$ with any two values.

Subtituting between triangles

Substituting one triangle into the other lets you relate $P$ and $R$ without needing to find $V$ or $I$ first:

$P = I^2R$ $R = \frac{P}{I^2}$
$P = \frac{V^2}{R}$ $R = \frac{V^2}{P}$
$I = \sqrt{\frac{P}{R}}$ $V = \sqrt{PR}$
Example: Solving for $P$ when you're given $I$ and $R$

To solve for $P$ we need $I$ and $V$.

We know we can get $V$ from $I \times R$, values we have.

If we take $P = VI$ and substitue $V$ for $I \times R$, we get $P = (IR)I

Simplify, and we get $P = I^2R$

Doing this on the fly can be a lot. This video makes solving between the triangles a piece of cake.

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