Ohm's Law
Introduction: This article focuses on the nature of Ohm's Law, one of the most crucial equations in the electric world.
The Essentials
One concept that hasn't been explored is resistance. Resistance is the capacity of a given material to impede a given current. Resistance is used to facilitate the specs of a given circuit and dissipates heat. They're also used in other kinds of appliances, like space heaters, toasters, and irons.
Ohm's Law is described as the following equation:
where
V = the voltage in volts across the element
i = the current in amps
R = the resistance in ohms of the element
Figure 1. is a good example of how resistance, voltage, and current relate to each other
Figure 1: Ohm's Law Concept
As shown in the image and the equation, We see the relationship between each other. Voltage is the potential that is "pushing" the charges through a given resistor. The current is the flow of electrons through an element. The resistance is the nature of an element to resist the flow of charges.
We also can confirm that as voltage is increases, the current increases. As resistance increases, current decreases. Thus, voltage and current are directly proportional while resistance and current are indirectly proportional.
Another repsresentation of Ohm's Law can be found in Figure 2.
Figure 2: Ohm's Law Triangle
This is an easy way to know an equation given that we know what we are solving for using the shape of the triangle.For example, if we want to solve for \emph{V}
This is because if we cover up the V in the triangle, we are left with \emph{i} and \emph{R} right next to each other, so they are multipled together.
If we want to know about \emph{i}, then
Similar process, but cover up the i and we are left with \emph{V} on top and \emph{R} on the bottom, so \emph{i} is a fraction with \emph{V} and \emph{R}
Finally, if we want to know about \emph{R}, then
Same reasoning with solving for \emph{i} but now we cover up \emph{R}.
Example
Let's do a couple of examples to solidify our understanding of Ohm's Law.
Say we are given an element with resistance 1 k \( \Omega \) and a current of 2 A. What voltage is applied across this element?
Using Ohm's law, we get the following
According to Ohm's Law, 2000 V is the voltage across the element to fulfill both given specifications.
Let's do another example. Say we are given a voltage over an element is 30 V and current through it is 2 A. What is the resistance needed to fulfill these specs?
Let's solve for resistance given our values above.
This means in order for the voltage element to be 30 V with a current of 2 A through it, the resistor must be 15\( \Omega \).
Using and implementing Ohm's Law is pretty simple, yet is one of the most important equations to know when it comes to circuit analysis.
Practice
Problem 1.) Say an element has a current of 3 mA and resistance of 10 k\( \Omega \). What is the voltage across the element?
Problem 2.) Say an element has a voltage of 10 V and current of 2 A. What is the resistance of the element?
Problem 3.) Say an element has a Voltage of 15 V and a resistance of 15 k\( \Omega \). What is the current through the element?
Solutions:
{Problem 1 Solution.)
V = 30 V. The following equation should give this result
Problem 2 Solution.)
\( R = 5 \Omega \). This is done with this variation of Ohm's Law
Problem 3 Solution.)
i = 1 mA. This is done with ths variation of Ohm's Law.