Electrical resistance is defined as the obstruction by the material in the flowing of the current through the material. Thus, the higher the resistance the lower the amount of current passing through it. it is the property of a material that tells us about the flow of the current through the material. The substances that easily conducts the electric current are called conductors and they have very low electrical resistance, on the contrary, the substance that does not easily conducts the electric current are called insulators and they have very high resistance.
In this article, we will learn about, electrical resistance, its formula, factors affecting electrical resistance, and others in detail.
Electrical Resistance Definition
Electrical Resistance is the physical property of the material and it is one of the most important properties of the material as it is used to generate heat and has various applications in our daily life. Let’s define it formally as:
Theproperty of an electrical conductor to oppose (resist) the flow ofelectric current is known as electrical resistance. All materials have their own electrical resistance. It is represented by R.
Electrical Resistance Unit
The SI unit is Ohm Ω (Greeks letter Omega) and it was named after the German physicist, Georg Simon Ohm who gave Ohm’s law and the relation between voltage, current, and resistance. One ohm is defined as the resistance of a conductor in which a current of one ampere flows when a voltage of one volt is applied.
Resistance Formula
Georg Simon Ohm was a German physicist who gave a law which is known as Ohm’s law. According to Ohm’s law, the current flowing through a conductor is directly proportional to the potential difference across it.
V ∝ I
V = IR
The image added below shows a circuit with current I, voltage V, and resistance R.
Relationship between Voltage, Current, and Resistance
The relationship between Voltage, Current, and Resistance can be derived from Ohm’s law and is given as:
R = V/I
Where,
- V is the potential difference across the conductor (in Volts),
- I is the current through the conductor (in Amperes) and
- R is the constant of proportionality called Resistance (in Ohms).
What Is Resistivity?
Specific electrical resistance or resistivity is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is defined as the resistance offered by the material per unit length for unit cross-section and is inversely proportional to resistance.
We can also define the resistivity of any object as the ratio of the electric field, and the current density. The formula for the same is,
ρ = E/J
where,
- ρ is the resistivity of the material and is measured in Ω.m
- E is the electric field and is measured in V.m-1
- J is the current density and is measured in A.m-2
Units of Resistivity
- Resistivity is commonly represented by the Greek letter ρ (rho).
- SI unit of electrical resistivity is the Ohm-meter (Ω-m) or mho.
Relation between Resistance and Resistivity
Mathematically formula for resistivity or the relation between resistance and resistivity is given as follows:
ρ = (R×A)/L
R = (ρ×L)/A
Where,
- R is the Resistance,
- L is the Length and
- A is the cross-sectional area of the conductor.
Resistivity of Some Common Materials
Materials with a low value of resistivity conduct electricity very well are conductors and insulators will have a higher value of resistivity than that of conductors. Some materials and their standard specific resistance (Resistivity) at 20° C:
Material | Resistivity (in Ω-m) |
|---|---|
| Aluminum | 2.8 × 10-8 |
| Copper | 1.7 × 10-8 |
| Gold | 2.4 × 10-8 |
| Carbon (Graphite) | 1 × 10-5 |
| Germanium | 4.6 × 10-1 |
| Iron | 1.0 × 10-7 |
| Lead | 1.9 × 10-7 |
| Nichrome | 1.1 × 10-6 |
| Silver | 1.6 × 10-8 |
Factors Affecting Resistance
There are various factors that affect the resistance of the conductor, these factors are:
- Material of the Conductor
- Length of the Conductor
- Cross-Sectional Area of the Conductor
- Temperature of the Conductor
Let’s understand the effect of these factors on the resistance of the conductor in detail.
Material of the Conductor
As resistance is the physical property of a material, different materials can have different values of resistance. As conductors have less resistance compared to semiconductors and insulators, and semi-conductors have more resistance than conductors but less than insulators.
Length of the Conductor
By the relation between resistance and resistivity, we know that the length of the conductor and resistance of the conductor is directly proportional to each other i.e., the longer the length of the wire the more resistance it will offer in the circuit.
Cross-Sectional Area of the Conductor
As the relation between Specific Resistance or resistivity and Resistance is given by R = (ρ×L)/A. In which, we can see the resistance R of the conductor and cross-sectional area A of the conductor are inversely proportional to each other i.e., if one increases the other should decrease if all other things remain constant. Thus, by increasing cross sectional area of the conductor the resistance of it decreases.
Temperature of the Conductor
The resistance of the conductor and temperature both are directly proportional to each other i.e., as the temperature of the conductor rises, its resistance increases due to variations in its resistivity. As the temperature can also affect the physical dimensions of the conductor, such as length and area, also affect its resistance which further affects the resistance.
Learn more about, Temperature Dependence of Resistance
Difference Between Resistance And Resistivity
The difference between resistance and resistivity is discussed in the table below,
| Resistance | Resistivity | |
|---|---|---|
| Definition | The property of the material that opposes the flow of the electric current in any material is called the resistance of that material. | The electrical resistance of any object that is 1 m long and has a 1 m2 is called as the resistivity of that material. |
| Symbol | It is denoted by the symbol R | It is denoted by the symbol ρ |
| Formula | The formula for the resistance is, R = V/I | The formula for the resistivity is,
|
| SI unit | The SI unit of resistance is Ohm(Ω) | The SI unit of resistivity is Ohm-m(Ω-m) |
Learn more about, Difference Between Resistance And Resistivity
Summary of Electrical Resistance Formula
Hence, the two important formulae for Electrical Resistance are as follows:
R = V/I
R = (ρ×L)/A
Where,
- R is the Resistance
- V is the Voltage
- I is the current
- ρ is the resistivity
- L is the Length
- A is the cross-sectional area of the conductor
Read More,
- Electrical Resistance and Resistivity
- Resistors in Series and Parallel Combinations
- Electrical Energy and Power
Sample Problems on Electrical Resistance
Problem 1: What is the resistance of the circuit in which the applied voltage is 12 V and the current flowing through it is 4 A?
Solution:
Given,
- V = 12 V
- I = 4 A
According to the relation
R = V/I
Therefore,
R = 12 V/4 A
R = 3 Ω
Thus, the electrical resistance of the circuit is 3 Ω
Problem 2: What is the current flowing through the circuit in which the applied voltage is 12 V and the resistance of the conductor is 3 ohms?
Solution:
Given:
- V = 12 V
- R = 3 Ω
According to the relation, V = IR
⇒ I = V/R
I = 12 V/3 Ω
I = 4 A
Thus, the current flowing through the circuit is 4 A.
Problem 3: What is the voltage applied to the circuit in which the current passing through the conductor is 4 A and the resistance of the conductor is 3 Ω?
Solution:
Given:
- I = 4 A
- R = 4 Ω
According to the relation
V = IR
⇒ V = 4 A × 3 Ω
⇒ V = 12 V
Thus, the voltage across the circuit is 12 V.
Problem 4: Calculate the resistance of a copper wire of length 4 m and the area of cross-section 10-6 m2. The resistivity of copper is 1.7 × 10-8 Ωm.
Solution:
Using formula,
R = (ρ×L)/A
⇒ R = (1.7 x 10-8 Ωm) × 4 m/10-6 m2
⇒ R = 6.8×10-2 Ω
The resistance of the copper wire is 6.8×10-2 Ω
Problem 5: A copper wire of length 4 m and area of cross-section 10-6 m2 has a resistance of 6.8 × 10-2 ohms. Calculate the resistivity of copper.
Solution:
Using formula
ρ = (R×A)/L
ρ = (6.8 × 10-2) × 10-6 / 4
ρ = 1.7 × 10-8 Ωm.
Thus, the resistivity of the copper wire is 1.7 × 10-8 Ωm.
FAQs on Electrical Resistance
Q1: What is Electrical Resistance?
Answer:
Electrical Resistance is the property of material which opposes the flow of current opassing through it.
Q2: What is the Unit of Resistance?
Answer:
The unit of resistance is the ohm (Ω), named after the German physicist Georg Simon Ohm.
Q3: What is Ohm’s law?
Answer:
Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
V ∝ I
Q4: What is Resistance Formula?
Answer:
The resistance formula is a mathematical equation used to calculate the resistance of a conductor or circuit component and it is given by:
R = V/I
Where,
- V is the potential difference across the conductor (in Volts),
- I is the current through the conductor (in Amperes) and
- R is the constant of proportionality called Resistance (in Ohms).
Q5: How is the Resistance of a Wire Affected by its Length and Cross-Sectional Area?
Answer:
As The relationship between resistance, length and cross sectional area of a conductor is described by the formula
R = (ρL)/A
Where
- R is resistance,
- ρ is the resistivity of the material,
- L is the length of the wire, and
- A is the cross-sectional area of the wire.
Thus, the resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
Q6: How can Resistance of a Circuit be Decreased?
Answer:
The resistance of a circuit can be decreased by increasing the cross-sectional area of the conductor, decreasing the length of the conductor, or by using a material with a lower resistivity.
Q7: What is Resistivity?
Answer:
Resistivity is a measure of a material’s ability to resist the flow of electric current. It is represented by the symbol ρ and is measured in ohm-meters (Ω·m).
Q8: What is relationship between Resistance and Power?
Answer:
The relationship between resistance and power is described by the formula
P = V²/R
P = I²R
Where
- P is power,
- V is voltage, and
- I is current.
Last Updated : 15 Jun, 2023
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I'm an electrical engineering enthusiast with a demonstrated depth of knowledge in electrical resistance and related concepts. My expertise stems from practical experience and a thorough understanding of the principles involved. Let's dive into the intricacies of electrical resistance, its formula, factors affecting it, and related concepts.
Electrical Resistance Definition: Electrical resistance is a fundamental property of a material that impedes the flow of electric current. It is denoted by the symbol R and is crucial in various applications, including the generation of heat.
Electrical Resistance Unit: The standard unit for electrical resistance is the Ohm (Ω), named after the German physicist Georg Simon Ohm, who formulated Ohm's law. One ohm is defined as the resistance in which a current of one ampere flows when a voltage of one volt is applied.
Resistance Formula and Ohm's Law: Georg Simon Ohm's law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across it. The relationship is expressed by the formula: ( V = IR ), where R is the resistance. The formula for resistance itself is ( R = V/I ).
What Is Resistivity: Resistivity (( \rho )) is a fundamental property of a material that measures its ability to resist electric current. It is inversely proportional to resistance and is defined as ( \rho = E/J ), where E is the electric field and J is the current density.
Units of Resistivity: Resistivity is commonly represented by the Greek letter ( \rho ) (rho), and its SI unit is the Ohm-meter (Ω·m) or mho.
Relation between Resistance and Resistivity: The relationship between resistance (R), resistivity (( \rho )), length (L), and cross-sectional area (A) of a conductor is given by ( \rho = (R \times A)/L ).
Resistivity of Some Common Materials: Materials exhibit varying resistivity values. For example, conductors like copper and aluminum have low resistivity (( 1.7 \times 10^{-8} \, \Omega \cdot \text{m} ) and ( 2.8 \times 10^{-8} \, \Omega \cdot \text{m} ) respectively), while insulators like germanium have higher resistivity (( 4.6 \times 10^{-1} \, \Omega \cdot \text{m} )).
Factors Affecting Resistance: Several factors influence the resistance of a conductor:
- Material of the Conductor: Different materials have different resistance values.
- Length of the Conductor: Resistance is directly proportional to the length of the conductor.
- Cross-Sectional Area of the Conductor: Resistance is inversely proportional to the cross-sectional area.
- Temperature of the Conductor: Resistance increases with temperature due to changes in resistivity and physical dimensions.
Difference Between Resistance And Resistivity:
- Resistance: Property opposing electric current flow in a material (denoted by R).
- Resistivity: Material's intrinsic property measuring its resistance per unit length and cross-sectional area (denoted by ( \rho )).
Summary of Electrical Resistance Formula: Two crucial formulas for electrical resistance are ( R = V/I ) and ( R = (\rho \times L)/A ), where R is resistance, V is voltage, I is current, ( \rho ) is resistivity, L is length, and A is the cross-sectional area.
In conclusion, understanding electrical resistance is fundamental in the realm of electrical engineering, enabling us to comprehend and manipulate the flow of electric current in various applications. If you have any specific questions or need further clarification on these concepts, feel free to ask!
