What is Resistance?
Resistance is a physical property of a material due to which, the material resists the flow of electricity through it. Resistance depends on the physical dimensions of the material, its composition, and temperature. The fundamental property resistivity or specific resistance is a measure of the resistance offered by a material. The resistance of a conductor is very low whereas insulators have very high resistances. The resistance of a conducting wire is proportional to its length and inversely proportional to its cross-sectional area. Resistance is a scalar quantity and it is expressed using a number with appropriate units. The SI unit of resistance is Ohm.
Definition of Resistance: Ohm’s Law
Ohm’s law states that the current flowing through a conductor is proportional to the potential difference between the two ends of the conductor, given that the temperature and other physical quantities remain constant. Mathematically, if the potential difference between the ends of a conductor is V, the current I flowing through it is,
I∝V
The proportionality constant is given by,
V/I = R
R is called the resistance of the conducting wire, which depends on the physical state and composition of the constituent material.
Dimension and Unit of Resistance Formula
The SI unit of resistance is Ohm(Ω), named after Georg 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 resistance of the conductor is defined as 1 Ohm.
1 Ω = 1V/1A
In terms of fundamental units, Ohm can be expressed as,
\[\Omega = \frac{J}{SA^{2}}\]
=kg.m2.s-3.A2
The dimension of resistance is \[ML2\]\[T-3\]\[I-2\].
International Ohm Unit Definition
The resistance of a column of mercury, which has a temperature of melting ice, uniform cross-sectional area, length of 106.3 cm, and mass of 14.4521 g, is called 1 Ohm.
SI Unit of Conductance
Electrical conductance is defined as the reciprocal of resistance. It is a property of a material that quantifies how easily 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
Specific Resistance
The resistance R of a conductor depends on its length L, cross-section A, and its composition. For a fixed cross-section, the resistance is proportional to the length of the conductor. Whereas the resistance is inversely proportional to the cross-section for a fixed length. These two dependencies can be written down combinedly as,
R∞L/A
R = pL/A
Here, is a proportionality constant, which is known as the specific resistance. The resistance of a homogeneous chunk of a material of unit length and unit cross-section is defined as the resistivity or specific resistance of the material. Quantitatively,
p = RA/L
The SI unit of specific resistance is Ohmm (Ω.m).
Resistance Unit Conversion Table
CGS unit of resistance is esu of resistance or statohm (stat Ω). It is related to ohm as,
1 Ω = 1V/1A
= (1/300statV)/(3×109statA)
= 1/9 X( 1011) stat Ω
1 stat Ω = 9 X 1011 Ω
Another unit of resistance is emu of resistance and it is related to ohm as,
1 emu of resistance = 1emuofpotential/1emuofcurrent
= 10-8V/10A
= 10-9Ω
Some Useful Units are listed Below
Solved Examples
A 5 mm diameter wire is produced from a chunk of metal. Another wire of diameter 1 cm is produced from an identical chunk. What is the ratio of the resistance of the two wires?
Resistance of a wire of length L and cross-section A is p/LA, which is the resistivity of the material. The mass and density of the chunk are m and D respectively. If the diameter of a wire of volume V is d,
A = πd2/4
V= m/D
L = V/A
Therefore, the resistance of a wire of diameter d is,
R = 16pm/πDd4
According to the problem, the mass and density of the two wires of diameters d1 = 5 mm=0.5cm and d2 =1 cm are the same such that the ratio of resistance is,
R1/R2 = (d2/d1)4
R1/R2 = (1cm/0.5cm)4
R1/R2 = 16
The ratio of the resistance of the wires is 16:1.
A parallel combination of two wires, made up of the same material, is connected to a battery. If the ratio of lengths and radii of the two wires are 4/3 and 2/3 respectively, what is the ratio of currents flowing through the wires?
Resistance of a wire of length L and radius r is,
R = pL/A = pL/πr2
where, is the resistivity of the material.
The ratio of lengths L1 and L2 of the two wires is,
L1/L2 = 43
The ratio of radii r1 and r2 of the two wires is,
r1/r2 = 23
Since the two wires are made up of the same material, the values are the same for both of them. The ratio of resistance r1 and r2 is
r1/r2 = (L1/L2).(r2r1)2
=(4/3). (3/2)2
= 3
In a parallel combination of resistors, the current flowing through one conductor is inversely proportional to its resistance i.e. the ratio of currents L1 and L2 is,
I1/I2 = R2/R1 = ⅓
The ratio of magnitudes of current flowing through the wires is 1:3.
Did You know?
Resistance depends on temperature. If other physical quantities are held constant, resistance increases with increasing temperature for metals. For glass, however, at very high temperatures, the resistivity decreases considerably.
Superconductors have zero resistance in the superconducting state (at very low temperatures).
The resistivity of semiconductors decreases with increasing temperature.
Why Should You Learn the Unit of Resistance - Ohm’s Law and Specific Resistance?
Learning the Unit of Resistance - Ohm’s Law and Specific Resistance will give you a better understanding of electric currents. These concepts will help you understand the different aspects of resistance and resistivity. Ohm’s law is one of the most important laws of physics, which is why you must have a strong grasp of this topic. Below are the reasons why you should learn:
It gives you a deep insight into some of the most crucial topics of the Physics subject.
It carries a significant weightage in your exam. So, to score well in the exam, you must know everything about resistance, Ohm’s law, and other concepts explained above.
Once you have learned it, you will be able to solve the important questions related to these topics.
If you do not know anything about it, you will not be able to study subsequent chapters of the Physics subject.
You can study the examples related to it provided above to understand how to solve different kinds of questions based on these concepts.
Learning Ohm’s law will help you understand the relationship between current, voltage, and resistance in an electric circuit. This way, you will be able to determine voltage, current, or resistance when any two of the quantities are given in the question.
Tips to start learning
It can be a tricky concept to learn. However, Vedantu provides you with a user-friendly learning platform to help you learn this topic with ease. You can use the following tips and tricks to start learning this unit:
While studying this unit, start making notes of the important points. These notes will come in handy during late revisions when you are preparing for your final exams.
After you are done with this, start solving important questions and questions that came in previous year papers.
Use Vedantu’s free learning platform to gain access to the notes and explanations of the Unit. These topics are explained by some of the best teachers at Vedantu to make the learning process smooth for students.
Refer to the examples related to this Unit to understand how to solve different types of questions in your exam.
Try to clear all the doubts to ensure that you have a clear understanding of every concept.
Find as many questions as possible to practice and strengthen your grip on the topics.
FAQs on Unit of Resistance
1. What is the SI unit of resistance and how is it defined according to CBSE 2025-26 syllabus?
The SI unit of resistance is the Ohm (Ω). It is defined as the resistance of a conductor in which a current of 1 ampere flows when a potential difference of 1 volt is maintained across its ends. Mathematically, 1 Ω = 1 V / 1 A.
2. How does resistance differ from resistivity in terms of definition and units?
Resistance quantifies how much a material opposes the flow of electric current and is measured in ohms (Ω). Resistivity (or specific resistance) measures the resistance of a material of unit length and unit cross-sectional area, and its SI unit is ohm-metre (Ω·m). While resistance depends on dimensions and material, resistivity is a property of the material itself.
3. What is Ohm’s Law and how is it applied to solve circuit problems?
Ohm’s Law states that the current (I) through a conductor is directly proportional to the potential difference (V) across it, provided temperature remains constant. The law is mathematically expressed as V = IR, where R is resistance. To solve circuit problems, use this formula to calculate any missing quantity if the other two are known.
4. Can you explain how the resistance of a wire changes with length and cross-sectional area, as per CBSE?
The resistance (R) of a wire increases proportionally with its length (L) and decreases with an increase in its cross-sectional area (A). Expressed mathematically: R = ρ (L/A), where ρ is the resistivity of the material. Doubling the length doubles the resistance, while doubling the cross-sectional area halves the resistance.
5. Why does resistance increase with temperature in metals but decrease in semiconductors?
In metals, increasing temperature causes atoms to vibrate more, which scatters the electrons and increases resistance. However, in semiconductors, higher temperature increases the number of free charge carriers, which reduces resistance. Thus, temperature affects resistance differently in metals and semiconductors due to differences in their atomic structure and carrier dynamics.
6. What are the derived units and dimensional formula of resistance in Physics?
The derived unit of resistance in terms of fundamental units is kg·m2·s-3·A-2. The dimensional formula for resistance is [ML2T-3I-2].
7. How are different units of resistance (stat ohm, emu ohm, ohm) related?
Ohm (Ω) is the SI unit. Stat ohm (CGS unit) and emu ohm (electromagnetic unit) relate to ohm as:
- 1 Ω = 1/9 × 1011 stat Ω
- 1 emu ohm = 10-9 Ω
8. What is electrical conductance and how is it connected to resistance?
Electrical conductance is the reciprocal of resistance. It measures how easily electricity flows through a material. Its SI unit is Siemens (S) or mho, with the relation Conductance (G) = 1/R (where R is resistance).
9. Why is understanding the unit of resistance important for scoring well in CBSE Physics exams?
Unit of resistance questions test conceptual clarity, application, and analytical thinking in Physics. They form the basis for understanding advanced electrical chapters and often carry significant marks. Mastery helps solve direct calculation as well as HOTS-based board questions, which improves overall exam performance.
10. What if two wires of equal mass and material have different diameters? How does their resistance compare?
If two wires of identical mass and material are made with different diameters, their resistance is inversely proportional to the fourth power of the diameter. Specifically, R₁/R₂ = (d₂/d₁)4, where d₁ and d₂ are the diameters. This significant variation shows that even small changes in diameter can greatly affect resistance.
11. How does resistance in superconductors differ from ordinary conductors?
In ordinary conductors, resistance is always greater than zero and increases with temperature. Superconductors, when cooled below a certain critical temperature, exhibit zero resistance, allowing current to flow without any energy loss.
12. Can you explain a misconception students often have about resistance and resistivity?
A common misconception is that resistance and resistivity are the same. Resistance depends on both material and shape (length, area) of a conductor, while resistivity is a property of the material only, unaffected by the sample’s shape or size.
13. What strategies should students adopt to master the topic ‘Unit of Resistance’ for board exams?
- Understand core definitions (resistance, resistivity, conductance).
- Practice formula-based questions (using Ohm’s law, R = ρL/A).
- Use units conversion problems to reinforce concepts.
- Analyze application-based and HOTS questions from previous year board papers.
- Revise diagrams and graphical representations related to resistance and resistivity for clarity.
