Ohm’s law states that the current flowing in a resistor is directly proportional to the voltage across the resistor. It can be mathematically expressed as

$I\propto V\ I=\frac { 1 }{ R } V$

Where, I, is the current in the resistor, V is the voltage across the resistor and R is the resistance of the resistor.

Ohm’s law is one of the basic electrical engineering laws. It provides a relationship between voltage V and current, I, such that current is dependent on voltage.

Ohm’s law is one of the basic electrical engineering laws. It provides a relationship between voltage V and current, I, such that current is dependent on voltage.

## Ohm’s Law Formula:

The above statement means that if we gradually increase the voltage across a conductor the flow of current will also change with a constant ratio, as the graph presents below.

The above graph and statement can be represented mathematically as follow:

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$$I \quad \propto quad V$

$I\quad =\quad \frac { 1 }{ R } V$

Converting the proportionality into an equation leads to a constant “R”, known as *Resistance.*

## Ohm’s Law Chart

The voltage, current, and resistance formula can be easily obtained from the following chart based on the given and required parameters.

The relationship can be rearranged to determine any element if the other two are given, as the ohm’s laws triangle represents.

## Ohm’s Law Calculator:

Enter any two parameters to calculate the third one in the ohm’s law calculator.

## Fluid Analogy:

Let us consider a tank filled with water at a certain height with an opening at the bottom. If the water level is higher inside the tank, more water will flow out of the tank. Or, if the water level inside the tank is low, less water will flow out of the tank. Similarly, Ohm’s law relates voltage (water level) and current (water flow) to behave in the same way.

## Current, Voltage and Resistance Relationship:

The current and voltage are directly related to each other. As you increase one of them, the second will also increase for maintaining a constant resistance of the circuit. Where resistance has an inverse relation with current and direct relation with voltage.

## Resistance and Conductance:

The term Resistance can be defined as: “The amount of opposition provided by a conductor or any other component in the path of current flow, is known as resistance.” If we use units of current and voltage in amperes and volts respectively, then the unit of resistance is called ohm (named after a scientist), which is equal to a volt per ampere and represented by Ω.

The inverse of resistance is *conductance,* which shows the ease of electric current passage. It is represented by “G”, and its unit is *mho (inverse of an ohm), *represented by ℧. Nowadays its unit is represented by *Siemens S.*

## Resistivity and conductivity:

Resistance is dependent on the material used for conduction and varies from material to material. Some materials may flow more current than others for the same amount of voltage. The property of materials to oppose electric current is called *resistivity*, also known as *specific resistance*.

The resistance of a wire depends upon some factors like its length, cross-section area, and the material used in the wire. Resistance is directly proportional to the length of wire and indirectly proportional to the square of the cross-section area, as shown in the diagram.

$R\propto l$

$R\quad \propto \quad \frac { 1 }{ A^{ 2 } } $

$R=ρ\frac { l }{ { A }^{ 2 } } $

$G\propto { A }^{ 2 }$

$G\quad \propto \quad \frac { 1 }{ l } $

$R=\sigma \frac { { A }^{ 2 } }{ l } $

Here ρ is the resistivity of the material. Its unit is ohm-meter (Ω-m). Where σ is the conductivity of the material and its unit is Siemens per meter.

## Ohm’s Law in AC:

Ohm’s is not directly applicable to the AC circuits, which involve inductors, capacitors, and/or transmission lines. The law can only be used for pure resistive AC circuits without any alterations. In the RLC AC circuit, the total opposition to the current is impedance Z, which is the combination of two orthogonal elements resistance and reactance.

Inductive Reactance : $\quad X_{ L }=2πfL\quad $

Capacitive Reactance: $\quad X_{ C }=\frac { 1 }{ 2\pi fC } \quad \quad $

Impedance: $\quad Z=\sqrt { { R }^{ 2 }+{ ({ X }_{ L }\sim { X }_{ C }) }^{ 2 } } \quad \quad $

Ohm’s Law for AC: $\quad I\quad =\quad \frac { V }{ Z } $

C represents the total capacitance of the circuit, L represents the total inductance of the electrical circuit and f represents the frequency of the AC source.

## Ohmic and Non-Ohmic Components:

Ohmic components are those which obey Ohm’s law for all values of voltage, current, negative and positive. Precisely saying, the value of R=V/I remains unchanged over long-range i.e. resistors.

Where in non-Ohmic components where R=V/I varies the value of voltages and/or currents i.e. diodes. \(\)

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## Conclusion:

Ohm’s law is a very basic and important tool in electrical engineering. The above discussion clarifies that current is directly proportional to voltage. Multiple resistors can be combined to get a specific current.

I REALLY APPRECIATE THE NOTES ARE VERY GOOD

excellent.