Unit of Resistance: Definition, Dimension, Formula

The unit of resistance is ohm denoted by the symbol Ω. ​Resistance is the opposition created by a substance against the flow of current. Resistance is expressed by the ratio of the voltage applied to the electric current that flows through it. When an electric current flows through a bulb, the bulb provides some obstructions to the flow of current which is known as electrical resistance. 

Key Terms: Resistor, SI Unit of Resistance, Unit of Resistivity, Unit of Specific Resistance, Ohm Unit, Ohm’s law, Bulb, Resistance, Conductor, Electric current

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Definition of Resistance: Ohm’s Law

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According to Ohm’s law, the electric current flowing through a conductor is proportional to the potential difference between the two ends of the conductor.

• Ohm’s law holds true only if we keep all other physical quantities and temperatures constant.
• The potential difference is written as V, and the current passing through the conductor is represented by I. 
• The unit of resistance is Ohm which also is derived using Ohm’s law.
• The resistance of a conducting wire depends upon the constituent material's physical state and composition.

So:

Ohm’s Law

Discover about the Chapter video:

Current Electricity Detailed Video Explanation:

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SI Unit of Resistance

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The SI unit of resistance is Ohm(Ω), which is represented as Volt per Ampere.

• The resistance of the conductor will be 1 Ohm if 1 A of current flows through the ends of a conductor when the two ends are kept at 1 V of potential difference.
• The SI unit of resistance is Ohm (Ω) named after George Ohm.
• Based on the above equation, it can be defined as:

1Ω = \(1V \over 1A \)

• 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].

\(\Omega = {V \over A}= {1 \over S}= {W \over A^2}= {V^2 \over W}= {s \over F}= {J.s \over C^2}= {kg.m^2 \over s.C^2}= {J \over s.A^2}= {kg.m^2 \over s^3.A^2}\)

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

The video below explains this:

Resistance Formula Detailed Video Explanation:

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SI Unit of Conductance

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Electrical conductance is referred to as the reciprocal of resistance which is a property of a material and it quantifies how easily the current can conduct through the material. The SI unit of conductance in siemens (S) or mho, which is the inverse of ohm, is the SI unit of electrical resistance.

mho = 1/Ohm = A/V

Read More: Unit of Resistance Important Questions

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Specific Resistance

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A conductor’s resistance R relies on its length L, cross-section A, and its composition. The resistance is proportional to the length of the conductor for a fixed cross-section. While the resistance is inversely proportional to the cross-section for a fixed length. It can be written as,

R \(\propto\) L/A

R = pL/A

Here, length and cross-sectional area are proportionality 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).

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Popular Resistance Units

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Some useful conversion units of resistance are – 

Check out:

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Things to Remember

• The physical quantity resistance is dependent on temperature, resistance increases with increasing the temperature.
• Zero resistance is recorded for superconductors.
• Ohm is the unit of resistance.
• 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.
• 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.

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Previous Year Questions

1. The resistance of a wire is ′R′ ′ ohm. If it is melted and stretched to ′n′ times its original length, its new resistance will be… [NEET 2017]
2. If the ammeter has a coil of resistance 480ohm and a shunt of 20ohm , the reading in the ammeter will be… [NEET 2015]
3. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be… [NEET 2003]
4. The internal resistance of the battery is… [NEET 2011]
5. An aluminium rod and a copper rod are taken such that… [DUET 2007]
6. In the adjacent shown circuit, a voltmeter of internal resistance… [BITSAT 2009]
7. A wire of resistance 12 ohm is in the form of a circle… [JIPMER 1999]
8. A cell of constant emf first connected to a resistance… [BITSAT 2006]
9. In an a.c. circuit the e.m.f. (∈) and the current (i) at any instant… [NEET 2008]
10. A circuit contain two resistors R1 and R2 in series… [JIPMER 2019]
11. Which of the following Material has lowest resistivity… [UPSEE 2016]
12. Specific resistance of a conductor material increases with… [COMEDK UGET 2009]
13. Two resistances A and B have colour codes orange, blue, white and brown… [COMEDK UGET 2015]
14. In the circuit shown the equivalent resistance between A and B is
15. Two batteries of emf 4V and 8V with internal resistance
16. A material B has twice the specific resistance of
17. The length of a conductor is halved. Its conductivity will be
18. The masses of three copper wires are in the ratio
19. To increase the range of an ammeter, we need to connect a suitable
20. Two electric bulbs, one of 200V, 40W and the other of