State and Explain Ohm’s Law Formula: Voltage, Current and Resistance

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

Ohm Law Key points

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.

Ohm Law Graph

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

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

Converting the proportionality into equation lead into 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 given and required parameters.

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

Ohm Law Calculator:

Enter any two parameters to calculate the third one.

Voltage V

Resistance R

Current I

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, the 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, the Ohm’s law relates voltage (water level) and current (water flow) behaves in the same way.

Ohm law explanation
Flow of water depends upon the level of water in tank

Current, Voltage and Resistance Relationship:

The current and voltage 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 is amperes and volts respectively, then the unit of resistance is called ohm (named after scientist), which is equal to volt per ampere and represent with 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 materials. 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 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 law Conductor cross section

Ohm's Law in AC:

Ohm’s is not directly applicable to the AC circuits, which involves inductors, capacitors and/or transmission lines. The law can only be used for pure resistive AC circuits without any alterations. In 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 } \quad \quad $

C represents the total capacitance of the circuit, L represents the total inductance of the electrical circuit and f represent the frequency of 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 remain unchanged over long rang i.e. resistors.
Where in non-Ohmic components where R=V/I vary the value of voltages and/or currents i.e. diodes. \(\)

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.

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  1. LWANDE February 6, 2019

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