SI unit of Resistance : Definition, Concept, Formula and Dimension

SI Unit of Resistance Overview

The SI unit resistance is the ohm, represented by the symbol Ω. It refers to the opposition a material presents to the flow of an electric current. Resistance is calculated as the ratio of the voltage applied to the electric current flowing through it. For example, when an electric current flows through a light bulb, the bulb's resistance to the flow of current is known as its electrical resistance.

SI Unit of Resistance: What is Resistance?

Resistance is a measure of the opposition to the flow of electric current in a conductor. It is expressed in Ohms (Ω) and is the property of a material that resists the flow of electric current. The amount of resistance in a material depends on various factors, including its composition, length, cross-sectional area, and temperature. When an electric potential difference is applied across a material with resistance, a current will flow through it, and the amount of current is proportional to the potential difference and inversely proportional to the resistance. Resistance is an important concept in electrical engineering and physics, as it plays a crucial role in the operation of electrical circuits and devices.

SI Unit of Resistance: Definition According to Ohm's Law

Ohm's law states that the current flowing through a conductor is proportional to the voltage difference between its ends, given that other physical quantities and temperatures remain constant. The voltage difference is denoted by "V" and the current is denoted by "I." The ohm, the unit of resistance, can be derived from Ohm's law. The resistance of a conducting wire is affected by the material it's made of and its physical state.

So, the formula is:

V∝I

VI = R, 

VI = Constant R = Resistance of the conducting wire

Also Read- Limitations of Ohm's Law

SI Unit of Resistance

The standard unit of resistance in the International System of Units (SI) is the ohm (Ω). It is defined as the amount of resistance in a conductor that will cause a current of one ampere to flow through it when a potential difference of one volt is applied across its ends.

The formula for calculating the resistance of a conductor can be derived from Ohm's law, which states that the current flowing through a conductor is proportional to the voltage difference across its ends. This relationship is described mathematically as follows:

V = IR

where:

1. V is the voltage difference across the conductor (in volts)
2. I is the current flowing through the conductor (in amperes)
3. R is the resistance of the conductor (in ohms).

This equation can be rearranged to find the resistance of a conductor given the voltage difference and current flowing through it:

R = V/I

It is important to note that the resistance of a conductor can depend on various factors such as temperature, length, cross-sectional area, and the material it is made of. Therefore, the resistance of a conductor can change with time, and it is crucial to keep these factors constant when measuring resistance.

SI Unit of Resistance: Derivation of Resistance

Ohm's law states that V = IR.

When three resistors are connected in series, the same current flows through each resistor, but the voltage drop varies. If V is the applied voltage and V1, V2, and V3 are the voltages across the resistances R1, R2, and R3, respectively, then

V=V1+V2+V3...(1)

Ohm's law states that V = IR

Req=R1+R2+R3

As a result, the equivalent resistance or total resistance of the circuit can be defined as a single value of resistance that can replace any number of resistors connected in series without changing the value of the circuit's current or voltage.

If we have n series resistances, the generalized formula for equivalent resistance is

Req= R1+R2+R3.......+Rn

We already know that the applied voltage is (v)

∴V=V1+V2+V3 ∴V=V1+V2+V3

We also know that

V = IR (from ohm's law) 

∴IReq= IR1+IR2+IR1 

∴IReq= IR1+IR2+IR1

⇒IReq= I(R1+R2+R3)⇒IReq= I(R1+R2+R3)

⇒R1+R2+R3

As a result, the equivalent resistance or total resistance of the circuit can be defined as a single value of the resistor connected in series while changing the values of the circuit's current or voltage.

SI Unit of Resistance: Dimensional Formula

The dimensional formula of ohm is [Ω], which stands for "kilogram meter squared per second squared per ampere squared." This formula represents the physical dimensions of resistance, which are related to the amount of force that opposes the flow of electric current in a conductor. The formula is derived from the formula for resistance, which is the voltage difference across a conductor divided by the current flowing through it. 

The dimensional formula of voltage is:  

Ω = VA=1S=WA2=V2W=sF=J.sC2=kg.m2s. C2=Js.A2=k.m2s3.A2

Here, the following stands for:

•  A = ampere
• S = siemens
• V = volt
• W = watt
• s = second
• m = meter
• J = joule
• F = farad 
• kg = kilogram 
• C = coulomb

Also Read- Resistance Formula

SI Unit of Conductance

The SI unit of conductance is the Siemens (S). It is the reciprocal of resistance, and represents the ease with which an electric current flows through a material. One Siemens is defined as the amount of conductance that allows a current of one Ampere to flow through a material with a resistance of one Ohm. The unit is named after the German inventor and engineer Werner von Siemens.

mho = 1/Ohm = A/V

SI Unit of Resistance: Specific Resistance

The resistance of a conductor, represented by R, is determined by factors such as its length (L), its cross-sectional area (A), and its composition. When the cross-sectional area is constant, the resistance is directly proportional to the length of the conductor. Conversely, when the length is fixed, the resistance is inversely proportional to the cross-sectional area. This relationship can be expressed as:

R ∝L/A

R = pL/A

Here, length and cross-sectional area are proportionally constant, which is known as the specific resistance. The resistance of a homogeneous material of unit length and unit cross-section is defined as the resistivity or specific resistance of that material. Quantitatively, 

p = RA/L

The SI unit of specific resistance is Ohm (Ω. m).

SI Unit of Resistance: Common Resistance Units

Some useful conversion units of resistance are – 

Also Read- SI Unit of Acceleration

SI Unit of Resistance: Types of Resistance

There are several types of resistance, each with its own formula:

1. Electrical resistance: This type of resistance is a measure of the opposition to the flow of electric current in a conductor. It is calculated using Ohm's Law, which states that the resistance of a material is equal to the voltage applied across it divided by the current flowing through it:
   R = V / I

Where R is the resistance in Ohms (Ω), V is the voltage in Volts (V), and I is current in Amperes (A).

1. Thermal resistance: This type of resistance is a measure of the opposition to the flow of heat through a material. It is calculated using the formula:
   R = ΔT / Q

Where R is the thermal resistance in kelvin per watt (K/W), ΔT is the temperature difference across the material in kelvins (K), and Q is the heat flow through the material in watts (W).

1. Acoustic resistance: This type of resistance is a measure of the opposition to the flow of sound through a material. It is calculated using the formula:
   R = P / Q

Where R is the acoustic resistance in rayls (Pa·s/m^4), P is the sound pressure in pascals (Pa), and Q is the flow rate of sound energy in watts (W).

SI Unit of Resistance: Difference between Resistance And Resistivity

Also Read- SI Unit of Impulse

SI Unit of Resistance: Things to Remember

• The resistance of a homogeneous material of unit length and unit cross-section is defined as the resistivity or specific resistance of that material. Quantitatively, p = RA/L.
• The physical quantity resistance is dependent on temperature, resistance increases with increasing temperature.
• Ohm is the unit of resistance.
• Zero resistance is recorded for superconductors.
• In terms of fundamental units, Ohm can be expressed as Ω = J/ S. A2 = kg. M2. s-3. A-2
• The dimensional formula of Ohm is [ML2T-3I-2].
• Ohm's law states that the current flowing through two points of a conductor is directly proportional to the voltage across two points.

Also Read: