Conductivity

11. Which one among the following is the correct representation of the ele

Which one among the following is the correct representation of the electric field when a conducting spherical shell is placed between the plates of a parallel plate capacitor ?

Subscribe on YouTube
Diagram (a)
Diagram (b)
Diagram (c)
Diagram (d)
This question was previously asked in
UPSC Geoscientist – 2024
Download PDFAttempt Online
The correct option is B.
Inside a conductor in electrostatic equilibrium, the electric field is zero. Electric field lines must be perpendicular to the surface of a conductor. In a parallel plate capacitor, the field is uniform between the plates in the absence of the sphere. When a conducting sphere is introduced, induced charges on its surface redistribute the field lines.
Diagram (b) shows the electric field lines entering and leaving the conducting spherical shell. Key features correctly depicted are:
1. The electric field lines are absent inside the conducting shell, indicating zero electric field within the conductor.
2. The electric field lines are perpendicular to the outer surface of the conducting shell at all points where they meet the surface.
3. The field lines are distorted by the presence of the conductor, originating from the positive plate, terminating on the induced negative charges on the near side of the sphere, originating again from the induced positive charges on the far side of the sphere, and finally terminating on the negative plate.
Diagrams (a) and (d) are incorrect as they show electric fields inside the conductor. Diagram (c) is incorrect as the field lines are not perpendicular to the conductor’s surface.

Join Our Telegram Channel

12. Which one of the following semi-conductors possesses the highest value

Which one of the following semi-conductors possesses the highest value of band gap Eg?

Subscribe on YouTube
Si
Ge
GaAs
PbS
This question was previously asked in
UPSC Geoscientist – 2023
Download PDFAttempt Online
The band gap (Eg) values for the given semiconductors are approximately:
Si (Silicon): ~1.1 eV (indirect band gap)
Ge (Germanium): ~0.67 eV (indirect band gap)
GaAs (Gallium Arsenide): ~1.42 eV (direct band gap)
PbS (Lead Sulfide): ~0.37 eV (direct band gap)
Comparing these values, GaAs has the highest band gap among the options.
The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. This value is a key characteristic of semiconductor materials.
Semiconductors are classified by their band gap, which can be direct or indirect. A larger band gap generally means the material is less conductive. Materials with larger band gaps (e.g., GaN, SiC) are used in high-power, high-temperature, and high-frequency applications, as well as in blue/UV light emitters.

Join Our Telegram Channel

13. Which one of the following is the most appropriate reason for aircraft

Which one of the following is the most appropriate reason for aircraft being equipped with conducting tyres ?

Join Our Telegram Channel
They can transfer the charge accumulated on their surfaces during lightning
They can transfer the charge accumulated on their surfaces being rubbed by air particles
They can transfer accumulated on their surfaces due to inflight operation of several gadgets
For preventing sparks on the ground while they land
This question was previously asked in
UPSC CDS-2 – 2024
Download PDFAttempt Online
The most appropriate reason for aircraft being equipped with conducting tyres is for preventing sparks on the ground while they land.
Aircraft build up a considerable amount of static electric charge during flight due to friction with air, dust, and precipitation. This charge needs to be safely dissipated upon landing. Conducting tyres provide a low-resistance path for this accumulated static charge to flow from the aircraft’s structure to the ground, thus neutralizing the charge gradually and preventing a sudden electrostatic discharge or spark that could ignite flammable fuel vapours near the ground.
Option B correctly identifies the source of the charge accumulation (rubbing by air particles), and conducting tyres *do* transfer this charge. However, the *reason* for this capability is the safety outcome described in option D – preventing potentially catastrophic sparks during landing. Option D is the most direct and crucial reason for the design feature.

Subscribe on YouTube

14. A metal wire of length l and diameter d has a resistance R. What would

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ?

Join Our Telegram Channel
R
R/4
R/2
2R
This question was previously asked in
UPSC CDS-2 – 2022
Download PDFAttempt Online
The resistance (R) of a wire is given by the formula R = ρ(L/A), where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = π(d/2)^2 = πd^2/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R ∝ 1/d^2).
If the diameter is doubled (2d), the new area becomes A’ = π(2d)^2/4 = π(4d^2)/4 = πd^2. This means the area becomes four times the original area (A’ = 4A).
Since R ∝ 1/A, the new resistance R’ will be R’ = R / (A’/A) = R / 4.
– Resistance is inversely proportional to the cross-sectional area of the wire.
– Cross-sectional area is proportional to the square of the diameter.
The resistivity (ρ) depends on the material of the wire, which is stated as the same in the question. The length (L) is also stated as the same. Therefore, only the change in diameter affects the resistance in this case.

Subscribe on YouTube

15. Which one of the following pairs of metals are very good conductors of

Which one of the following pairs of metals are very good conductors of heat ?

Join Our Telegram Channel
Silver and Copper
Silver and Lead
Copper and Mercury
Lead and Mercury
This question was previously asked in
UPSC CDS-2 – 2022
Download PDFAttempt Online
Heat conductivity is the ability of a material to conduct heat. Metals are generally good conductors of heat. Among common metals, silver is the best conductor of heat, followed closely by copper. Both silver and copper are widely used in applications where high thermal conductivity is required. Lead and mercury, while metals, are significantly poorer conductors of heat compared to silver and copper. Therefore, the pair of metals that are very good conductors of heat is Silver and Copper.
Silver and Copper are excellent conductors of heat.
Thermal conductivity values (approximate, W/(m·K) at room temperature): Silver (~429), Copper (~401), Aluminum (~205), Iron (~80), Lead (~35), Mercury (~8.3). This data confirms that Silver and Copper are indeed among the best heat conductors.

Subscribe on YouTube

16. Two wires are made having same length l and area of cross-section A. W

Two wires are made having same length l and area of cross-section A. Wire 1 is made of copper and wire 2 is made of aluminium. It is given that the electrical conductivity of copper is more than that of aluminium. In this context, which one of the following statements is correct?

Join Our Telegram Channel
The resistance of wire 1 will be higher than that of wire 2.
The resistance of wire 2 will be higher than that of wire 1.
The resistance of both the wires will be the same.
If same current is flown through both the wires, the power dissipated in both the wires will be the same.
This question was previously asked in
UPSC CDS-2 – 2017
Download PDFAttempt Online
The resistance of wire 2 will be higher than that of wire 1.
The resistance (R) of a wire is inversely proportional to its electrical conductivity (σ) for a given length (l) and area of cross-section (A). The formula is R = (1/σ) * (l/A). Since both wires have the same length and area of cross-section, their resistances are directly proportional to their resistivities (ρ = 1/σ). We are given that the electrical conductivity of copper (wire 1) is more than that of aluminium (wire 2), i.e., σ_Cu > σ_Al. This implies that the resistivity of copper is less than that of aluminium (ρ_Cu < ρ_Al).
Since R = ρ * (l/A) and l and A are the same for both wires, R is proportional to ρ. As ρ_Cu < ρ_Al, it follows that R_1 (copper) < R_2 (aluminium). Therefore, the resistance of wire 2 (aluminium) is higher than that of wire 1 (copper). Power dissipated is given by P = I²R or P = V²/R. If the same current flows, power dissipated is proportional to resistance. If the same voltage is applied, power dissipated is inversely proportional to resistance.

Subscribe on YouTube

17. What is the correct sequence of resistivity of silver, nichrome and gl

What is the correct sequence of resistivity of silver, nichrome and glass at room temperature ?

Subscribe on YouTube

[amp_mcq option1=”Silver < Nichrome < Glass" option2="Glass < Nichrome < Silver" option3="Silver < Glass < Nichrome" option4="Nichrome < Silver < Glass" correct="option1"]

This question was previously asked in
UPSC CDS-1 – 2022
Download PDFAttempt Online
Resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. Materials are classified as conductors, semiconductors, or insulators based on their resistivity values.
Good electrical conductors have very low resistivity. Metals like silver are excellent conductors. Alloys like nichrome are generally poorer conductors than pure metals and have higher resistivity. Insulators have very high resistivity, effectively preventing current flow. Glass is a good insulator. Therefore, the correct order of resistivity from lowest to highest is Silver (conductor) < Nichrome (alloy) < Glass (insulator).
At room temperature, the resistivity values are approximately: Silver ~ 1.59 × 10⁻⁸ Ω·m, Nichrome ~ 1.1 × 10⁻⁶ Ω·m, Glass ~ 10¹⁰ to 10¹⁴ Ω·m. This confirms the order: Silver < Nichrome < Glass. Nichrome's relatively high resistivity makes it suitable for heating elements in appliances like toasters and heaters.

Join Our Telegram Channel

18. Which one of the following is an electric conductor ?

Which one of the following is an electric conductor ?

Join Our Telegram Channel
A plastic sheet
Distilled water
Human body
A wooden thin sheet
This question was previously asked in
UPSC CDS-1 – 2021
Download PDFAttempt Online
An electric conductor is a material that allows electric current to flow through it easily. Plastic and wood are electrical insulators, meaning they resist the flow of electricity. Distilled water is a very poor conductor of electricity because it contains very few ions. The human body contains various salts dissolved in water, which provide ions that can carry electric charge, making the human body a conductor of electricity.
Conductors allow charge flow, insulators resist it. The presence of free charge carriers (like ions in solutions or free electrons in metals) determines conductivity.
Metals like copper and aluminum are excellent conductors. Pure water is a poor conductor; its conductivity increases significantly with dissolved impurities (salts, acids, bases) that form ions.

Subscribe on YouTube

19. We are given three copper wires of different lengths and different are

We are given three copper wires of different lengths and different areas of cross-section. Which one of the following would have highest resistivity ?

Subscribe on YouTube
Copper wire of 50 cm length and 1 mm diameter
Copper wire of 25 cm length and 0.5 mm diameter
Copper wire of 10 cm length and 2.0 mm diameter
All the wires would have same resistivity
This question was previously asked in
UPSC CDS-1 – 2021
Download PDFAttempt Online
Resistivity is a fundamental property of a material that describes its resistance to electrical conduction. It depends only on the nature of the material and its temperature, not on its dimensions (length or area of cross-section).
– The resistance (R) of a wire is given by the formula R = ρ * (L/A), where ρ is the resistivity, L is the length, and A is the area of cross-section.
– While the resistance (R) of the copper wires will be different because they have different lengths and diameters, their resistivity (ρ) will be the same because they are all made of the same material (copper) and are presumably at the same temperature.
– Resistance is an extrinsic property that depends on both the material’s resistivity and its physical dimensions.
– Resistivity is an intrinsic property specific to the material itself.

Join Our Telegram Channel

20. Two metallic wires made from copper have same length but the radius of

Two metallic wires made from copper have same length but the radius of wire 1 is half of that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes

Subscribe on YouTube
2R
R/2
5R/4
3R/4
This question was previously asked in
UPSC CDS-1 – 2018
Download PDFAttempt Online
The resistance of a wire is given by R = ρ * (l/A), where ρ is the resistivity, l is the length, and A is the cross-sectional area. The area A = πr², where r is the radius.
For wire 1, with radius r1 and length l, the resistance R1 = ρ * l / (πr1²). We are given R1 = R.
For wire 2, with the same length l but radius r2 = 2 * r1 (since r1 is half of r2, r2 is double r1), the resistance R2 = ρ * l / (πr2²) = ρ * l / (π(2r1)²) = ρ * l / (π * 4r1²) = (1/4) * [ρ * l / (πr1²)].
Since R = ρ * l / (πr1²), we have R2 = R/4.
When the two wires are joined in series, the total resistance is the sum of individual resistances: R_total = R1 + R2.
R_total = R + R/4 = 5R/4.
– Resistance is inversely proportional to the square of the radius (R ∝ 1/r²), assuming constant length and material.
– When conductors are in series, their resistances add up (R_total = R1 + R2 + …).
Resistivity (ρ) is a material property. Since both wires are made of copper, they have the same resistivity. The formula for resistance is derived from Ohm’s law and material properties. In series connection, the current is the same through both components, and the total voltage across the combination is the sum of voltage drops across each component.

Join Our Telegram Channel
Page 1Page 2Page 3Page 4Page 5