Class 10th Science Chapter 11 – Electricity | Resistance and Factors Affecting Resistance

⚡ Electricity

Resistance and Factors Affecting Resistance

प्रतिरोध एवं प्रतिरोध को प्रभावित करने वाले कारक

Class 10 Science | CBSE + Foundation + Competitive

⚡ Resistance and Factors Affecting Resistance

1. Introduction | परिचय

Electric current does not flow through every conductor with equal ease. Every conductor offers some opposition to the flow of electric charge. This opposition is called electrical resistance.

विद्युत धारा के प्रवाह का किसी चालक द्वारा किया गया विरोध विद्युत प्रतिरोध (Electrical Resistance) कहलाता है।

Resistance → Opposition to the flow of electric current
प्रतिरोध → विद्युत धारा के प्रवाह का विरोध

2. Resistance | प्रतिरोध

Resistance is denoted by the symbol R. According to Ohm's law:

R = V/I

where:

• R = Resistance
• V = Potential difference
• I = Electric current

The SI unit of resistance is ohm (Ω).

3. Meaning of One Ohm

A conductor has a resistance of 1 ohm when a potential difference of 1 volt produces a current of 1 ampere through it.

1 Ω = 1 V / 1 A

Thus:

Ω = V/A

4. Resistance as Opposition to Current

For a fixed potential difference:

I = V/R

Therefore, larger resistance means smaller current, while smaller resistance means larger current.

Resistance	Current at Same V
Small	Large
Large	Small

5. Factors Affecting Resistance

The resistance of a conductor depends mainly on:

1. Length of conductor (L)
2. Area of cross-section (A)
3. Nature/material of conductor
4. Temperature

The first three are represented by the relation:

R = ρL/A

6. Resistance Depends on Length

For a conductor made of the same material and having the same cross-sectional area:

R ∝ L

Therefore, resistance increases when the length of the conductor increases.

Length	Resistance
L	R
2L	2R
3L	3R
L/2	R/2

7. Why Does Longer Wire Have More Resistance?

When the length of a wire increases, electrons have to travel through a greater distance and experience more interactions with the atoms of the material.

Therefore, opposition to charge flow increases.

Longer wire → More resistance

8. Resistance Depends on Area of Cross-Section

For the same material and same length:

R ∝ 1/A

Thus, resistance is inversely proportional to the area of cross-section.

Area	Resistance
A	R
2A	R/2
3A	R/3
A/2	2R

9. Effect of Length and Thickness

10. Nature of Material

Different materials offer different amounts of resistance to the flow of electric current.

This property is represented by a quantity called resistivity (ρ).

For example, copper has low resistivity and is therefore widely used for electrical wiring.

Low resistivity → Good conductor
High resistivity → Poor conductor / greater resistance for same dimensions

11. Resistivity | विशिष्ट प्रतिरोध

Resistivity is a property of a material that indicates how strongly the material opposes the flow of electric current.

It is represented by the Greek letter ρ (rho).

R = ρL/A

Rearranging:

ρ = RA/L

SI unit of resistivity:

Ω m

12. Derivation of R = ρL/A

Experimentally, for a uniform conductor:

R ∝ L

and:

R ∝ 1/A

Combining both:

R ∝ L/A

Introducing the material-dependent constant ρ:

R = ρL/A

13. Physical Meaning of Resistivity

If a material has resistivity ρ, then a uniform specimen of that material having:

• Length = 1 m
• Cross-sectional area = 1 m²

would have resistance numerically equal to its resistivity.

Resistivity is a property of the material and does not depend on the size of the sample itself, although the resistance of the sample does.

14. Resistance vs Resistivity

Resistance (R)	Resistivity (ρ)
Depends on length	Property of material
Depends on area	Independent of sample dimensions
Depends on material	Depends on material
SI unit: Ω	SI unit: Ω m
For a given conductor, R can change with dimensions	ρ characterises the material at a given temperature

15. Effect of Temperature on Resistance

Temperature can affect resistance. For most metallic conductors, resistance increases when temperature increases.

Therefore:

Temperature ↑ → Resistance ↑

For many metals, approximately over a suitable temperature range:

R_T = R₀[1 + α(T-T₀)]

where α is the temperature coefficient of resistance.

At Class 10 level, remember mainly: For metals, resistance generally increases with temperature.

16. Animated Concept: Four Factors

17. Formula for Resistance

R = ρL/A

Symbol	Meaning	SI Unit
R	Resistance	Ω
ρ	Resistivity	Ω m
L	Length	m
A	Cross-sectional area	m²

18. Effect of Changing Length

Example: A wire has resistance 5 Ω. What will be its resistance if its length is doubled, keeping material and cross-sectional area unchanged?

Since:
R ∝ L

New resistance:
R' = 2R
R' = 2 × 5
R' = 10 Ω

19. Effect of Changing Area

Example: A wire has resistance 12 Ω. Its cross-sectional area is doubled. Find the new resistance.

Since:
R ∝ 1/A

When area doubles:
R' = R/2
R' = 12/2
R' = 6 Ω

20. Effect of Both Length and Area

Example: A wire has resistance R. Its length becomes 3 times and area becomes 2 times. Find the new resistance.

R = ρL/A

New resistance:
R' = ρ(3L)/(2A)
R' = 3R/2

Thus resistance becomes 1.5 times the original value.

21. Why Are Electric Wires Made of Copper or Aluminium?

Copper and aluminium have relatively low resistivity and therefore offer relatively low resistance when used with suitable dimensions.

They allow electric current to flow efficiently and are therefore commonly used as conducting materials.

Copper is especially common in electrical wiring because of its good conductivity and useful mechanical properties.

22. Why Are Heating Elements Made of Alloys?

Heating-element materials such as nichrome are chosen because they have relatively high resistivity and can withstand high temperatures.

A higher resistance helps electrical energy to be converted into thermal energy when current flows.

Examples: electric heater, toaster, iron, electric kettle.

23. Why Are Connecting Wires Thick?

A thicker wire has a larger cross-sectional area.

R = ρL/A

Thus, for the same material and length, increasing area decreases resistance.

Thick wire → Large area → Lower resistance

24. 30 MCQs | बहुविकल्पीय प्रश्न

Q1. The SI unit of resistance is:

A. Ohm

B. Volt

C. Ampere

D. Watt

Answer: A

Q2. Resistance is the opposition to:

A. Heat

B. Electric current

C. Mass

D. Time

Answer: B

Q3. The correct relation is:

A. R = VI

B. R = I/V

C. R = V/I

D. R = V+I

Answer: C

Q4. Resistance of a uniform wire is directly proportional to:

A. Area

B. Length

C. 1/Length

D. Current only

Answer: B

Q5. Resistance is inversely proportional to:

A. Length

B. Resistivity

C. Cross-sectional area

D. Voltage

Answer: C

Q6. The formula for resistance of a uniform conductor is:

A. R = ρA/L

B. R = ρL/A

C. R = LA/ρ

D. R = L/(ρA)

Answer: B

Q7. The SI unit of resistivity is:

A. Ω

B. Ω/m

C. Ω m

D. V/m

Answer: C

Q8. If length of a wire is doubled, its resistance becomes:

A. Half

B. Double

C. Four times

D. Unchanged

Answer: B

Q9. If cross-sectional area is doubled, resistance becomes:

A. Half

B. Double

C. Four times

D. Unchanged

Answer: A

Q10. Which quantity is a property of the material?

A. Resistance

B. Current

C. Resistivity

D. Voltage

Answer: C

Q11. For most metals, resistance with increasing temperature:

A. Increases

B. Decreases

C. Becomes zero

D. Never changes

Answer: A

Q12. A thicker wire of the same material and length has:

A. Higher resistance

B. Lower resistance

C. Infinite resistance

D. Zero length

Answer: B

Q13. Copper is commonly used for electrical wires because it has:

A. High resistivity

B. Low resistivity

C. No electrons

D. Infinite resistance

Answer: B

Q14. Nichrome is commonly used in heating elements because of its:

A. Very low resistivity only

B. Relatively high resistivity and high-temperature suitability

C. Zero resistance

D. Very low melting point

Answer: B

Q15. If both length and area are doubled, resistance becomes:

A. R/2

B. 2R

C. R

D. 4R

Answer: C

Q16. If length is tripled while area remains constant:

A. R becomes R/3

B. R becomes 3R

C. R becomes 9R

D. R remains R

Answer: B

Q17. If area becomes four times, resistance becomes:

A. 4R

B. 2R

C. R/4

D. R

Answer: C

Q18. Resistivity mainly depends on:

A. Material and temperature

B. Length only

C. Area only

D. Current only

Answer: A

Q19. A conductor has V = 10 V and I = 2 A. Its resistance is:

A. 2 Ω

B. 5 Ω

C. 10 Ω

D. 20 Ω

Answer: B

Q20. A 5 Ω resistor carries 3 A. Potential difference is:

A. 8 V

B. 15 V

C. 2 V

D. 1.67 V

Answer: B

Q21. A wire has resistance R. If its length is halved and area unchanged:

A. 2R

B. R/2

C. R

D. R/4

Answer: B

Q22. A wire's area is reduced to half. Its resistance becomes:

A. R/2

B. R

C. 2R

D. 4R

Answer: C

Q23. Which formula represents resistivity?

A. ρ = RA/L

B. ρ = RL/A

C. ρ = L/RA

D. ρ = A/RL

Answer: A

Q24. Resistance of a wire depends on:

A. Length

B. Area

C. Material

D. All of these

Answer: D

Q25. The resistance of a conductor is 20 Ω. If voltage is 40 V, current is:

A. 0.5 A

B. 2 A

C. 20 A

D. 800 A

Answer: B

Q26. A material with low resistivity is generally:

A. A good conductor

B. A poor conductor

C. An insulator only

D. A vacuum

Answer: A

Q27. Which change decreases resistance of a uniform wire?

A. Increasing length

B. Decreasing area

C. Increasing area

D. Increasing resistivity

Answer: C

Q28. If length becomes 4 times and area becomes 2 times, resistance becomes:

A. 2R

B. R/2

C. 4R

D. 8R

Answer: A

Q29. Which has SI unit Ω m?

A. Resistance

B. Resistivity

C. Conductance

D. Current

Answer: B

Q30. For a metal, increasing temperature generally:

A. Decreases resistance

B. Increases resistance

C. Makes resistance exactly zero

D. Has no effect

Answer: B

25. 30 Subjective Questions with Answers

2 Marks Q1. Define electrical resistance.

Electrical resistance is the opposition offered by a conductor to the flow of electric current. It is represented by R and measured in Ω.

2 Marks Q2. Write the formula for resistance.

R = V/I.

2 Marks Q3. What is the SI unit of resistance?

Ohm (Ω).

2 Marks Q4. What is resistivity?

Resistivity is a material property that characterises the opposition of a material to current flow. It is represented by ρ.

2 Marks Q5. Write the SI unit of resistivity.

Ohm metre (Ω m).

3 Marks Q6. State the factors affecting resistance.

Resistance depends on length, cross-sectional area, material/resistivity and temperature.

3 Marks Q7. How does length affect resistance?

For the same material and area, R ∝ L. Therefore doubling length doubles resistance.

3 Marks Q8. How does area affect resistance?

For the same material and length, R ∝ 1/A. Therefore increasing area decreases resistance.

3 Marks Q9. Why are thick wires preferred for carrying large currents?

Thick wires have larger cross-sectional area, which gives lower resistance and hence reduces unwanted heating and voltage drop.

3 Marks Q10. Differentiate resistance and resistivity.

Resistance depends on dimensions and material, whereas resistivity is a property of the material at a specified temperature.

4 Marks Q11. Derive R = ρL/A.

For a uniform conductor:
R ∝ L
R ∝ 1/A
Therefore R ∝ L/A.
Introducing proportionality constant ρ:
R = ρL/A.

4 Marks Q12. Explain the effect of material on resistance.

Different materials have different resistivities. For the same length and area, a material with greater resistivity gives greater resistance.

4 Marks Q13. Explain the effect of temperature on metallic resistance.

For most metals, resistance increases as temperature increases because higher temperature increases opposition to electron transport.

4 Marks Q14. Why is copper used for electrical wiring?

Copper has relatively low resistivity and therefore provides low resistance for suitable wire dimensions. It also has useful mechanical and practical properties.

4 Marks Q15. Why are alloys used in heating appliances?

Alloys such as nichrome have relatively high resistivity and can withstand high temperatures, making them suitable for heating elements.

5 Marks Q16. Explain all factors affecting resistance with equations.

Resistance depends on:
1. Length: R ∝ L
2. Area: R ∝ 1/A
3. Material: represented by resistivity ρ
4. Temperature: changes resistance, especially in metals.
Combining length, area and material:
R = ρL/A.

5 Marks Q17. Explain resistivity and its SI unit.

Resistivity is a property of a material that indicates its opposition to current flow. From R = ρL/A:
ρ = RA/L.
Its SI unit is Ω m.

5 Marks Q18. Why does a longer wire have greater resistance?

A longer conductor provides a longer path for charge carriers. For the same material and cross-sectional area, R ∝ L, so increasing length increases resistance.

5 Marks Q19. Why does a thicker wire have lower resistance?

A thicker wire has larger cross-sectional area. Since R ∝ 1/A, increasing area decreases resistance.

5 Marks Q20. Explain why resistance is not the same as resistivity.

Resistance is the resistance of a particular conductor and depends on its dimensions as well as material. Resistivity is a characteristic property of the material at a specified temperature.

6 Marks Q21. A wire has resistance 10 Ω. Its length is doubled without changing material or area. Find new resistance.

R ∝ L.
R' = 2R = 2 × 10
R' = 20 Ω.

6 Marks Q22. A wire has resistance 16 Ω. Its area is doubled. Find new resistance.

R ∝ 1/A.
R' = R/2 = 16/2
R' = 8 Ω.

6 Marks Q23. A wire has resistance 6 Ω. Its length becomes 3 times and area becomes 2 times. Find new resistance.

R'/R = (L'/L)/(A'/A)
= 3/2
R' = 6 × 3/2
R' = 9 Ω.

6 Marks Q24. A wire of length 2 m has area 1 × 10⁻⁶ m² and resistivity 1.7 × 10⁻⁸ Ω m. Find resistance.

R = ρL/A
= (1.7 × 10⁻⁸ × 2)/(1 × 10⁻⁶)
= 3.4 × 10⁻² Ω
R = 0.034 Ω.

6 Marks Q25. A conductor has resistance 12 Ω at 6 V. Find current.

I = V/R
= 6/12
I = 0.5 A.

6 Marks Q26. A 5 Ω resistor carries 4 A current. Calculate voltage.

V = IR
= 4 × 5
V = 20 V.

6 Marks Q27. A wire's length is doubled and its area is halved. Find the ratio of new resistance to old resistance.

R'/R = (2L/L)/(A/2A)
= 2 × 2
R'/R = 4.
New resistance is four times the original.

6 Marks Q28. Two wires have the same material and length. Wire A has twice the area of Wire B. Compare their resistances.

R ∝ 1/A.
Therefore:
R_A/R_B = A_B/A_A
= 1/2.
Thus Wire A has half the resistance of Wire B.

6 Marks Q29. Two wires have the same material and area. Wire A is three times longer than Wire B. Compare their resistance.

R ∝ L.
Therefore:
R_A/R_B = L_A/L_B = 3.
Thus Wire A has three times the resistance.

6 Marks Q30. Explain why resistance of a metallic wire changes when it is heated.

Heating increases the temperature of the metal. The increased temperature changes the interaction of charge carriers with the lattice and generally increases resistance in metals. Therefore the resistance is temperature dependent.

26. Assertion–Reason

Q1. Assertion: Resistance of a wire increases when its length increases, provided other factors remain constant.
Reason: R ∝ L.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q2. Assertion: Increasing cross-sectional area decreases resistance.
Reason: R ∝ 1/A.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q3. Assertion: Resistivity and resistance have the same SI unit.
Reason: Resistivity is given by ρ = RA/L.

Answer: Assertion is false; Reason is true.
Resistance unit = Ω; resistivity unit = Ω m.

Q4. Assertion: For most metals, resistance increases with temperature.
Reason: Temperature affects the electrical resistance of metals.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q5. Assertion: A thick wire of the same material and length has lower resistance.
Reason: A thicker wire has larger cross-sectional area.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

27. HOTS | Higher Order Thinking

HOTS 1. A wire has resistance R. It is stretched so that its length becomes twice its original length while its volume remains constant. What happens to its resistance?

Volume = LA remains constant. If L becomes 2L, area becomes A/2.
R'/R = (2L/L)/(A/2A) = 4.
Resistance becomes four times.

HOTS 2. Why does stretching a wire increase its resistance even though it is still made of the same material?

Its resistivity remains the same if temperature is unchanged, but stretching increases length and decreases cross-sectional area. Both changes increase resistance according to R = ρL/A.

HOTS 3. Two wires have equal resistance but different materials. Can their lengths and areas be different?

Yes. Since R = ρL/A, different resistivities can be compensated by different length-to-area ratios.

HOTS 4. Why does a high-resistivity material generally produce greater resistance for the same dimensions?

From R = ρL/A, for fixed L and A, resistance is directly proportional to resistivity.

HOTS 5. A student says, "Resistance depends only on material." Is the statement correct?

No. Resistance depends on material, length, cross-sectional area and temperature. Resistivity, rather than resistance, is primarily a material property at a specified temperature.

28. Important Comparison Table

Change	Effect on R
Length doubles	R doubles
Length becomes half	R becomes half
Area doubles	R becomes half
Area becomes half	R doubles
Length ×3	R ×3
Area ×3	R/3
Length ×2, Area ×2	R unchanged
Length ×2, Area ÷2	R ×4
Length ×3, Area ×2	R ×1.5

29. CBSE Golden Points ⭐

1. Resistance is the opposition to electric current.
2. R = V/I.
3. SI unit of resistance is ohm (Ω).
4. For a uniform conductor, R = ρL/A.
5. Resistance is directly proportional to length.
6. Resistance is inversely proportional to cross-sectional area.
7. Resistivity is represented by ρ.
8. SI unit of resistivity is Ω m.
9. Resistivity is a material property at a specified temperature.
10. Resistance depends on dimensions as well as material.
11. For most metals, resistance increases with temperature.
12. Copper and aluminium are commonly used as conductors.
13. Nichrome and similar alloys are useful for heating elements.
14. Thick wire has lower resistance than a thin wire of the same material and length.
15. Long wire has greater resistance than a short wire of the same material and area.

30. Memory Tricks 🧠

🔹 Trick 1 — L-A Rule

L ↑ → R ↑
Length बढ़े → Resistance बढ़े

A ↑ → R ↓
Area बढ़े → Resistance घटे

🔹 Trick 2 — Formula

R = ρL/A

Think:
ρ and L ऊपर, A नीचे.

🔹 Trick 3 — Material

ρ = Material Property

🔹 Trick 4 — Wire

Long + Thin → High Resistance
Short + Thick → Low Resistance

🔹 Trick 5 — Unit

R → Ω
ρ → Ω m

31. One-Minute Revision ⚡

⚡ Resistance = Opposition to current.

📐 R = V/I.

📏 R ∝ L.

⭕ R ∝ 1/A.

🧪 Material → Resistivity ρ.

📘 R = ρL/A.

📏 Resistivity unit = Ω m.

🔌 Resistance unit = Ω.

🔥 Metals: Temperature ↑ → Resistance ↑.

⚡ Long + Thin wire → More resistance.

⚡ Short + Thick wire → Less resistance.

32. Concept Map

⚡ Electric Current
↓ 🧱 Resistance R
↓ R = ρL/A
↓ 📏 Length L
↓ L ↑ → R ↑

⭕ Cross-sectional Area A
A ↑ → R ↓

🧪 Material
ρ determines resistance

🔥 Temperature
Metal: T ↑ → R ↑

33. Final Summary | अंतिम सारांश

The resistance of a conductor is its opposition to the flow of electric current.

R = V/I

For a uniform conductor:

R = ρL/A

Thus resistance:

• increases with length,
• decreases with cross-sectional area,
• depends on the material through resistivity,
• and changes with temperature.

For most metallic conductors, resistance increases with increasing temperature.

Longer → More R   |   Thicker → Less R

⚡ R = ρL/A → Resistance depends on Material, Length and Area

⚡ Electricity

Resistance and Factors Affecting Resistance

प्रतिरोध एवं प्रतिरोध को प्रभावित करने वाले कारक

Class 10 Science | CBSE + Foundation + Competitive