Anjali Mishra Content Writer-SME
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Resistivity or electrical resistance is a fundamental property that measures the extent to which the flow of current can be opposed. It is independent of geometric properties of a material such as shape and size.
- Resistivity only depends on the temperature and is represented by the symbol ‘ρ’ (read as rho).
- Resistivity Formula is given as
| \(ρ = {RA \over l}\) |
Here, R is the Resistance of the conductor, A is the cross-section area, and l is the length of the conductor.
- The reciprocal value of electrical Resistivity is called Electrical Conductivity which is denoted by σ (read as sigma).
- It is used as one of the parameters for comparing two or more than two current carrying materials.
Read More: Resistivity Formula Important Questions
| Table of Content |
Key Terms: Resistivity, Resistivity Formula for Semiconductors, Resistance, Conductor, Electric Current, Metals, Insulators, Semiconductors, Resistivity Formula, Ohm-meter, Temperature, Low resistivity
What is Resistivity Formula?
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Resistivity is the resistance of a conductor of unit length and unit cross-sectional area at a particular temperature. It is defined as a property of a material that depicts how strongly the material resists or conducts the electric current.
- Resistivity is denoted by the symbol ρ and has the SI unit ohm-meter (Ωm).
- It is the measurement of the ability of a material to oppose the flow of electric current.
- Materials that are good conductors of electricity have low resistivity such as metals.
- Insulators have very high resistivity such as rubber, glass, graphite, plastics, etc.
- Resistivity formula for semiconductor is given as:
| ρ = q *(neμe+ nhμh) |
ρ = Resistivity
q = Charge on electrons
ne = Density of conduction electrons
μe = Mobility of conduction electrons
nhDensity of holes
μh = Mobility of holes
- Their resistivity is affected by the presence of impurities in them and it decreases with the increase in temperature.
Discover about the Chapter video:
Current Electricity Detailed Video Explanation:
Read More:
| Relevant Concepts | ||
|---|---|---|
| Difference Between Resistance and Resistivity | Resistivity Temperature Dependence | Current Electricity |
| Unit of Resistance | Unit of Specific Resistance | Unit of Conductivity |
Resistivity Formula
Resistivity Formula for conductors with a uniform cross-section and uniform flow of electric current is given as follows:
| \(ρ = {RA \over l}\) |
Where
- ρ: Resistivity of the material in Ωm.
- R: Electrical resistance of the material in Ω
- l: Length of the material in m.
- A: Area of the cross-section of the material in m2.
Read More: Resistivity Formula MCQs
Solved ExampleExample: Find the resistivity of a wire with a length of 30cm and an area of 0.9 m2. The resistance of the given wire is 5Ω. Solution: It is given that
Using the Resistivity Formula ρ = RA/l ρ = (5 × 0.9)/0.3 = 15 Ωm Thus, the resistivity of the wire will be 15 Ωm. |
Resistivity Formula Derivation
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Resistance of a conductor is the product of the resistivity of the conductor and the length of the conductor divided by the conductor’s cross-sectional area.
Mathematically, Resistance Formula is expressed as
| \(R = {ρ} {l \over A}\) |
Where
- R: Resistance of the conductor.
- ρ: Resistivity of the conductor.
- l: Length of the conductor.
- A: Area of the cross-section of the conductor.
On rearranging the above equation, we get
RA = ρl
ρl = RA
It can be thus written as:
| \(ρ = {RA \over l}\) |
Thus, we can derive Resistivity Formula from the Resistance Formula.
Read More: Current Electricity Important Questions
Solved Examples on Resistivity Formula
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Given below are a few solved examples on the Resistivity Formula to grasp the concept better:
Example 1: What will be the resistivity of a material whose resistance is 2 Ω, the area of cross-section is 25cm2 and the length is 15 cm?
Solution: Given that
- Resistance R = 2 Ω
- Length l = 15 cm = 0.15 m
- Area A = 25 cm2 = 0.25 m2
Using the Resistivity Formula, we get
ρ = RA/l
ρ = (2 × 0.25)/0.15 = 3.333 Ωm
Therefore, the resistivity of the given material is 3.333 Ωm.
Read More: Current Electricity MCQs
Example 2: Find the resistivity of a wire whose length is 3m and has a diameter of 0.6 m with a resistance of 60 Ω.
Solution: According to the question,
- Resistance R = 60
- Length l = 3m
- Diameter = 0.6 m
So, Radius (r) = 0.3m
Area of cross-section = πr2 = 3.14 × (0.3 × 0.3) m2
Thus, Area A = 0.2826 m2
Using the Resistivity Formula,
ρ = RA / l
ρ = (60 × 0.2826)/3 = 5.652 Ωm
Thus, the resistivity of the given wire is 5.652 Ωm.
Read More: NCERT Solutions for Class 12 Physics Current Electricity
Factors Affecting Resistivity
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Resistivity is affected by various factors which are listed as follows:
- Resistivity of a conductor is directly proportional to its resistance. ρ ∝ R.
- It is directly proportional to the uniform cross-sectional area. ρ ∝ A.
- It is inversely proportional to the length of the material. ρ ∝ 1/l
- It depends upon the nature of the material and temperature too.
Read More:
| Related Topics | ||
|---|---|---|
| Relation Between Resistance And Length | Resistors in Series | Uses of Resistor |
| Resistor | Internal Resistance Formula | Types of Current |
Resistivity of Materials
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Resistivity of materials is explained as follows:
- Resistivity of Metals: When the temperature of the metallic wire is raised, its electric resistance increases. The resistivity of a pure metal is directly proportional to its absolute temperature.
- Resistivity of Alloys: The resistivity of alloys also increases with a rise in temperature, but this increase is much small compared to pure metals.
- Resistivity of Semiconductors: The resistivity of semiconductors decreases rapidly with a rise in temperature.
- Resistivity of Electrolytes: Resistivity of Electrolytes also decreases with a rise in the temperature.
Things to Remember
- Resistivity is the resistance of electric current from one end to the other end in any material.
- It is denoted by ρ and its SI unit is ohm-meter (Ωm).
- Resistivity Formula is ρ = RA/l, where R is the resistance, A is the area of cross-section, and l is the length of the conductor.
- It is directly proportional to the material resistance (R) and length (l).
- It is inversely proportional to the area of the cross-section (A) of the material.
- Good conductors of electricity have a low resistivity while insulators have a very high resistivity.
Previous Year Questions
- A stone of mass 5 kg falls from the top of a cliff 50 m high and buries into…
- A galvanometer with resistance 100 Ω gives full-scale deflection with…
- The resistance between any two terminals when connected in a triangle is…. [NEET 1993]
- An electric current of 3 A passes through a wire of resistance 15 Ohm. How much heat...
- Two copper wires, one of length 1 m and the other of length 9 m, are found to have…
- Just after key K is pressed to complete the circuit, the reading will be... [KEAM 1999]
- If a wire of resistance R = 10ohm is stretched to double its length, then the new resistance will...
- An AC voltage source of variable angular frequency ωand fixed amplitude…
- The resistance if a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length...
- A potential difference V is applied across a conductor of length ‘l’. How is the drift velocity affected when…
- Potential drop through 4Ω resistor is... [NEET 1993]
- The potential difference per unit length of the wire will be… [NEET 1999]
- Value of R for which the power delivered in it is maximum is given by... [NEET 1992]
Sample Questions
Ques 1. Define Resistivity. (3 Marks)
Ans. Resistivity is a property of a material that describes the extent to which it can oppose the flow of electric current through it. It shows how strongly it resists an electric current. A low resistivity shows that the material readily allows electric current while a high resistivity indicates that the material doesn’t allow the current to pass through it. Resistivity is denoted by the Greek letter ρ. Ohm-meter (Ωm) is the SI unit of Resistivity.
Ques 2. Find the resistivity of a wire whose length, area, and resistance are given as 0.2 m, 0.5 m2, and 3 Ω respectively. (3 Marks)
Ans. Given that
- R = 3 Ω
- l = 0.2 m and
- A = 0.5 m2
Using the Resistivity Formula, we get
ρ = RA / l
ρ = (3 x 0.5)/0.2 = 7.5 Ωm.
Thus, the resistivity of the given wire is 7.5 Ωm.
Ques 3. What factors affect electrical resistance? (3 Marks)
Ans. The electrical resistance of a conductor is affected by the following factors:
- Area of the cross-section of the conductor.
- Length of the conductor.
- Material of the conductor.
- Temperature of the conducting material.
Ques 4. Find out the resistivity of the metal wire of length 2 m and 0.6 mm diameter and resistance of 50 Ω. (3 Marks)
Ans. Given that
- Resistance (R) = 50 Ω
- Length (l) = 2 m
- Diameter = 0.6 mm
- Resistivity (ρ) =?
Therefore, the radius would be 0.3 mm = 3 × 10-4 m
Area of the cross-section of the wire = πr2
A = 3.14 × (3×10-4)2
A = 28.26 × 10-8 = 2.826 × 10-9 m2
Using the Resistivity Formula,
ρ = RA/l
ρ = (50 Ω × 2.826 ×10−9 m)/22m
ρ = 25 × 2.826 × 10-9 Ωm
ρ = 70.65 × 10-9 Ωm
Thus, the resistivity of the metal wire is 70.65 × 10-9 Ωm.
Ques 5. Describe the effect on the resistance of pure metals with an increase in temperature. (3 Marks)
Ans. The resistance of pure metals increases when there is a rise in temperature. The number of electrons in the conduction band increases due to the increase in temperature, reducing mobility and thereby increasing resistance. With the increase in temperature, the thermal motion among the atoms of the lattice also increases because of which the charge carriers bump more into the lattice vibrations. This in turn increases the resistivity of the pure metal.
Ques 6. What is the SI unit of Resistivity? (1 Mark)
Ans. The SI Unit of Resistivity is ohm-meter (Ωm).
Ques 7. What is Resistivity Formula? (3 Marks)
Ans. The Resistivity of a conductor can be calculated using the given formula:
\(ρ = {RA \over l}\)
Here,
Ques 8. What will be the resistivity of the material if the conductivity of the material is 4 ohm-1m-1? (3 Marks)
Ans. The conductivity (σ ) is given as 4 ohm-1m-1.
Using the Resistivity Formula,
ρ = 1/ σ
ρ = 1/4 Ωm
ρ = 0.25 Ωm
Thus, the resistivity will be 0.25 Ωm.
Ques 9. Name the element which has the highest resistivity. (1 Mark)
Ans. Nichrome has the highest resistivity (1.50 × 10-6 Ωm). It shows the heating effect of electric current because of its high resistance.
Ques 10. Silver has a resistivity of 1.6⋅10−8 Ωm. What would the total resistance be of a silver wire of length 0.5 m and radius 0.004 m? (5 Marks)
Ans. We will follow the given steps to find the resistivity of the silver wire.
Step 1: Identify the resistivity (ρ), length (L), and radius (r) of the wire.
- ρ = 1.6⋅10−8 Ωm
- L = 0.5 m
- r = 0.004 m.
Step 2: Calculate the cross-sectional area of the wire.
Use the equation for the area of a circle\(A=\pi r^2\),
\(A=\pi (0.004m)^2\)
\(A=5.0265 \cdot 10^{-5}m^2\)
The cross-sectional area of the wire is \(5.0265 \cdot 10^{-5}m^2\).
Step 3: Calculate the resistance of the wire.
Substitute the known values into the equation for resistance: \(R=\frac{\rho L}{A}\) and solve for resistance.
\(R=\frac{\rho L}{A}\)
\(R=\frac{(1.6\cdot 10^{-8}\Omega m)(0.5m)}{5.0265 \cdot 10^{-5}m^2}\)
\(R=1.592\cdot 10^{-4} \Omega\)
The resistance of the silver wire is \(1.592\cdot 10^{-4} \Omega\).
Ques 11. What is the difference between Resistivity and Resistance? (3 Marks)
Ans. Resistance of a material refers to the opposition of the flow of electrons in a material whereas resistivity is a property of a material that occurs when resistance is offered. Resistance is the ratio of voltage (V) to the current (I) applied to a material while resistivity is the ratio of the electric field (E) to the current density (J). The SI unit of resistance is ohms whereas resistivity is measured in terms of ohms meter.
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