Class 10 Chapter 1 Electricity Physics Solution S.Chand. Part 4

 Part 4

Very Short Answer Type Questions

1. As the conductor is made thicker, its resistance decreases. This is because thicker conductors have more cross-sectional area for the flow of electrons, reducing resistance.

2. If the length of a wire is doubled by taking more of the wire, its resistance also doubles. This is because resistance is directly proportional to the length of the wire.

3. The resistance of a conductor depends on several factors:

   - Length: Longer conductors have higher resistance.

   - Cross-sectional area: Conductors with larger cross-sectional areas have lower resistance.

   - Temperature: Generally, resistance increases with temperature.

   - Material: Different materials have different resistivities, affecting resistance.

4. Silver is the best conductor of electricity among commonly available materials.

5. Among iron and mercury, mercury is a better conductor of electricity.

6. Copper and aluminum wires are usually used for electricity transmission because:

   - They have relatively low resistivity, meaning they offer low resistance to the flow of electricity.

   - They are abundant and relatively inexpensive.

   - They have good mechanical properties for handling and installation.

7. The material used for making the heating element of an electric iron is usually nichrome.

8. Nichrome is a type of nickel-chromium alloy. One of its uses is as a heating element in appliances like toasters, electric irons, and hair dryers.

9. Two reasons why nichrome alloy is used for making the heating elements of electrical appliances:

   - Nichrome has a high melting point, allowing it to withstand the high temperatures generated during heating.

   - It has a relatively high resistivity, which enables it to produce significant heat when an electric current passes through it.

10. The coils of electric irons and electric toasters are made of an alloy rather than a pure metal because alloys like nichrome have:

    - Higher resistance compared to pure metals, which allows them to generate more heat when an electric current passes through them.

    - Higher melting points, making them more suitable for applications where high temperatures are required, such as heating elements in appliances.

11. 

   (a) A long piece of nichrome wire has more resistance compared to a short one. This is because resistance is directly proportional to the length of the wire.

   (b) A thin piece of nichrome wire has more resistance compared to a thick one. This is because resistance is inversely proportional to the cross-sectional area of the wire.

12. 

   (a) If the temperature of a pure metal decreases, its resistance typically decreases as well. This phenomenon is known as negative temperature coefficient of resistance. As the temperature decreases, the metal's atoms vibrate less, allowing electrons to flow more freely, thereby reducing resistance.

   (b) The presence of impurities in a metal can increase its resistance. Impurities can disrupt the regular arrangement of atoms in the metal lattice, causing more collisions with electrons as they move through the metal. This increases the resistance of the metal.

13.Fill in the following blanks with suitable words:

Resistance is measured in ohms. The resistance of a wire increases as the length increases; as the temperature increases; and as the cross-sectional area decreases.

Short Answer Type Questions

14. (a) The "resistivity" of a substance is a measure of its inherent resistance to the flow of electric current. It is a property that quantifies how strongly a material opposes the flow of electrical current. (b) Given: Length (l) = 1.0 m, Diameter (d) = 0.2 mm = 0.0002 m, Resistance (R) = 10 Ω. Using the formula: $�=\frac{�\cdot �}{�}$, where $�=�\cdot {\left(\frac{�}{2}\right)}^2$. Solving for resistivity (ρ): $�=\frac{�\cdot �}{�}=\frac{10\times �\times (0.0001{)}^2}{1.0}$ $�\approx 1.59\times 10^{-6}\mathrm{\Omega }\cdot \text{m}$.

15. (a) The expression for the resistance (R) of a metallic wire in terms of resistivity (ρ), length (l), and cross-sectional area (A) is given by $�=\frac{�\cdot �}{�}$. (b) Given: Length (l) = 2 m, Area of cross-section (A) = 1.55 × 10^(-6) m², Resistivity (ρ) = 2.8 × 10^(-8) Ωm. Using the formula $�=\frac{�\cdot �}{�}$: $�=\frac{2.8\times 10^{-8}\times 2}{1.55\times 10^{-6}}$ $�\approx 3.61\mathrm{\Omega }$.

16. (a) Two examples of substances which are good conductors of electricity are copper and silver. They are good conductors because they have many free electrons that can move easily in response to an electric field. (b) Given: Length (l) = 1.0 km = 1000 m, Diameter (d) = 0.50 mm = 0.0005 m, Resistivity (ρ) = 1.7 × 10^(-8) Ωm. Using the formula $�=\frac{�\cdot �}{�}$: $�=\frac{1.7\times 10^{-8}\times 1000}{�\times (0.00025{)}^2}$ $�\approx 54.40\mathrm{\Omega }$.

17. 17. Current will flow more easily through a thick wire of the same material when connected to the same source. This is because a thicker wire has a larger cross-sectional area, which offers less resistance to the flow of current compared to a thin wire.

18. (a) The resistance of a conductor is directly proportional to its length. So, the longer the conductor, the higher its resistance. (b) The resistance of a conductor is inversely proportional to the area of its cross-section. So, the larger the cross-sectional area, the lower its resistance. (c) The resistance of a conductor generally increases with temperature.

19. (a) Example: Copper has lower resistance compared to iron. This demonstrates that resistance depends on the nature of the material of the conductor. (b) Given: Length (l) = 10 km = 10,000 m, Diameter (d) = 2.0 mm = 0.002 m, Resistivity (ρ) = 2.7 × 10^(-8) Ωm. Using the formula $�=\frac{�\cdot �}{�}$: $�=\frac{2.7\times 10^{-8}\times 10000}{�\times (0.001{)}^2}$ $�\approx 0.687\mathrm{\Omega }$.

20. (a) Increasing the length of a metal wire increases its resistance. (b) Increasing the diameter of a metal wire decreases its resistance. (c) Increasing the temperature of a metal wire generally increases its resistance.

21. (a) The resistance of a wire is inversely proportional to its area of cross-section. So, as the area of cross-section increases, the resistance decreases. (b) The resistance of a wire is inversely proportional to the square of its diameter. So, as the diameter increases, the resistance decreases.

22. (i) When the length of a wire is tripled:

- The resistance of the wire will also triple. This relationship is directly proportional according to the formula $�=\frac{�\cdot �}{�}$, where $�$ is resistance, $�$ is resistivity, $�$ is length, and $�$ is the cross-sectional area.

(ii) When the diameter of a wire is tripled: - The resistance of the wire will decrease by a factor of $9$. This is because resistance is inversely proportional to the square of the diameter.

(iii) When the material of a wire is changed to one whose resistivity is three times: - The resistance of the wire will increase by a factor of $3$. This is because resistance is directly proportional to the resistivity of the material.

23.

23. 23. To calculate the area of cross-section (A) of the wire, we use the formula $�=\frac{�\cdot �}{�}$, where $�$ is resistance, $�$ is resistivity, $�$ is length, and $�$ is the cross-sectional area. Given:
    • Length (l) = 1.0 m
    • Resistance (R) = 23 Ω
    • Resistivity (ρ) = 1.84 × 10^(-6) Ωm Using the formula: $�=\frac{�\cdot �}{�}=\frac{1.84\times 10^{-6}\times 1.0}{23}$ $�\approx 8.00\times 10^{-8}{�}^2$

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• Long Answer Type Question

24. (a) Resistivity is a measure of a material's inherent resistance to the flow of electric current. It is defined as the resistance of a unit cube of the material. The expression for the resistivity ($�$) of a substance is given by: $�=\frac{�\cdot �}{�}$ Where:

• $�$ = resistivity of the substance (in ohm-meters, Ω·m)
• $�$ = resistance of the material (in ohms, Ω)
• $�$ = cross-sectional area of the material (in square meters, m²)
• $�$ = length of the material (in meters, m)

(b) The SI unit of resistivity is ohm-meter (Ω·m).

(c)

• Resistance (R) is the measure of opposition to the flow of electric current in a material. It depends on the dimensions of the material and its resistivity.
• Resistivity (ρ) is a material property that quantifies how strongly a material opposes the flow of electric current. It is independent of the dimensions of the material.

(d) Factors on which resistivity depends:

• Temperature: Resistivity generally increases with temperature for most materials.
• Material Composition: Different materials have different resistivities due to variations in their atomic and molecular structures.

Factors on which resistivity does not depend:

• Dimensions of the material: Resistivity is independent of the shape or size of the material.
• Applied voltage/current: Resistivity remains constant regardless of the voltage or current applied to the material.

(e) Given:

• Length (l) = 1 m
• Resistance (R) = 26 Ω
• Diameter (d) = 0.3 mm = 0.0003 m Using the formula for resistivity $�=\frac{�\cdot �}{�}$ and the formula for the area of cross-section $�=�\times {\left(\frac{�}{2}\right)}^2$, we can solve for resistivity: $�=�\times {\left(\frac{0.0003}{2}\right)}^2$ $�\approx 7.07\times 10^{-8}{�}^2$ $�=\frac{26\times 7.07\times 10^{-8}}{1}$ $�\approx 1.83\times 10^{-6}\mathrm{\Omega }\cdot \text{m}$
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Multiple Choice Questions (MCQs)

25. 25. The resistance of a wire can be calculated using the formula $�=\frac{�\cdot �}{�}$, where $�$ is resistance, $�$ is resistivity, $�$ is length, and $�$ is the cross-sectional area. Given:

• Length ($�$) = 300 m
• Cross-sectional area ($�$) = 1.0 mm² = $1.0\times 10^{-6}$ m²
• Resistivity ($�$) = $1.0\times 10^{-7}$ Ωm Using the formula: $�=\frac{1.0\times 10^{-7}\times 300}{1.0\times 10^{-6}}=30\mathrm{\Omega }$ So, the correct answer is option (d) 30 Ω.

26. 26. When the diameter of a wire is doubled, its resistance becomes:

• (c) one-half

27. 27. If the resistance of a certain copper wire is 1 Ω, then the resistance of a similar nichrome wire will be about:

• (c) 60 Ω

28. 28. If the diameter of a resistance wire is halved, then its resistance becomes:

• (c) one-fourth

29. 29. The resistivity of a certain material is 0.6 Ω m. The material is most likely to be:

• (c) a conductor

30. 30. When the area of cross-section of a conductor is doubled, its resistance becomes:

• (b) half

31. 31. The resistivity of copper metal depends on only one of the following factors. This factor is:

• (c) temperature

32. 32. If the area of cross-section of a resistance wire is halved, then its resistance becomes:

• (d) 4 times
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Questions Based on High Order Thinking Skills (HOTS)

33. When the length of a wire is increased to twice its original length, its resistance also doubles. This relationship is directly proportional. Therefore, if the original resistance was 20 Ω, the new resistance will be $20\times 2=40\mathrm{\Omega }$.

34. (a) For making electric wires, material Q would be the best choice. This is because it has the lowest resistivity among the given options, indicating it offers the least resistance to the flow of electric current. (b) For making a handle for a soldering iron, material P would be suitable. While resistivity is not the only factor to consider, a material with a relatively high resistivity like P would help prevent excessive heat transfer from the soldering iron to the handle. (c) For making solar cells, material R would be preferred. Solar cells require materials with high resistivity to maintain a potential difference and facilitate the generation of electricity when exposed to sunlight.

35. (a) A: Good conductor (b) B: Resistor (c) D: Insulator (d) C: Semiconductor

Reasoning:

• A has the lowest resistivity among the options, indicating it offers the least resistance to the flow of electric current, making it a good conductor.
• B has a very high resistivity, making it suitable for use as a resistor.
• D has a relatively high resistivity compared to A and C, indicating it would be an insulator, offering high resistance to the flow of electric current.
• C has a moderate resistivity, indicating it falls between conductors and insulators, suggesting it would be a semiconductor.

36. (a) Substance E (1.70 × 10^(-8) Ωm) is the best conductor of electricity among the given substances. This is because it has the lowest resistivity, indicating it offers the least resistance to the flow of electric current.

(b) Substance A (5.20 × 10^(-8) Ωm) is a better conductor compared to substance C (2.60 × 10^(-8) Ωm). This is because substance A has a lower resistivity, meaning it offers less resistance to the flow of electric current.

(c) Substance E (1.70 × 10^(-8) Ωm) would be advised to be used for making heating elements of electric irons. This is because a lower resistivity material like E would allow for more efficient flow of current, generating more heat and thus, heating up the iron faster.

(d) Substances E and C would be suitable for making electric wires. Both have relatively low resistivities compared to the others, meaning they offer lower resistance to the flow of electric current. This would ensure efficient transmission of electricity with minimal loss of energy in the form of heat.