Resistance Formula

This article discusses resistance along with the resistance formula and its derivation. Resistance refers to the amount that an object impedes or resists in an electric current. Electric current refers to the flow of electrons. An easier way to explain resistance is to consider an example of a person in a crowded market struggling to go from one shop to another. This situation is certainly similar to an electron trying to make its way through a wire.

What is Resistance?

Resistance refer to the property of materials that allow the flow of electric current. Resistance certainly opposes the flow of current. Furthermore, the unit of resistance is ohms which is represented by the Greek uppercase letter omega Ω. Moreover, the resistance depends on the voltage across a particular resistor and the current flowing through it. Resistance refers to a measure of the opposition to current flow in a particular electrical circuit.

The electrical resistance of an object refers to the measure of its opposition to the flow of electric current. The inverse quantity refers to the electrical conductance. Electrical conductance refers to the ease with which the passing of an electrical current passing takes place. Moreover, electric resistance shares some parallels with mechanical friction. Also, resistors refer to the components of the electric circuits. All the materials certainly resist current flow to a certain degree.

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Resistance Formula

The resistance formula is as follows:

Resistance = voltage drop across a resistor/ current flowing through a resistor

R = \(\frac{V}{I}\)
R = resistance (Ohms, Ω)
V = voltage difference which is between the two ends of a resistor (Volts, V)
I = the current which flows through a resistor (Amperes, A)

Resistance Formula Derivation

The derivation of the formula of resistance takes place from the Ohm’s law. This law states that the current density vector \(\vec{J}\) for some materials is parallel to the electrical field \(\vec{E}\), therefore
\(\vec{J}\) = \(\sigma \vec{E}\) = \(\frac{1}{P}\vec{E}\) (1)

Here, \(\sigma\) = 1/p refers to the conductivity of the material. This certainly is the inverse of the p, which is the resistivity. From this point, one must consider a material of a particular length L which involves two extreme cases of area A. Here application of a potential difference ΔV takes place. Therefore, by making use of the definition for potential difference, one can show:

\(\vec{E}\) = \(\frac{\Delta V }{L}\) (2)

One can certainly express the current flowing through the material as:

\(\vec{J}\) = \(\frac{I}{A}\) (3)

Now one must use the results of equations (2) and (3) on the equation (1), one can achieve:

\(\frac{I}{A}\) = \(\frac{1}{P}\) \(\frac{\Delta V }{L}\)
ΔV = \(I\frac{pL}{A}\)

So, when we talk of a typical relationship, ΔV = IR,
Then consequently R = \(\frac{pL}{A}\)

Solved Examples on Resistance Formula

Q1 In an electric circuit, a current of 4.00 A flows through a resistor. The voltage drop which takes place from one end of the resistor to the other happens to be 120 V. Find out the value of resistance?

A1 Applying the resistance formula

R = \(\frac{V}{I}\)
So, R = 120V/4A
R = 30.O Ω

Hence, the resistance of the resistor in the circuit is 30.0 Ω.