Conductivity Archives

21. A parallel-plate capacitor of capacitance C₁ is made using two gold pl

A parallel-plate capacitor of capacitance C₁ is made using two gold plates. Another parallel-plate capacitor of capacitance C₂ is made using two aluminium plates with same plate separation, and all the four plates are of same area. If ρg and ρa are respectively resistivities of gold and aluminium, then which one of the following relations is correct?

”C₁

”C₂

”C₁ρa

”C₁

This question was previously asked in

UPSC CDS-1 – 2017

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The capacitance of a parallel-plate capacitor is given by the formula C = ε * (A/d), where ε is the permittivity of the dielectric material between the plates, A is the area of one plate, and d is the distance between the plates.

– The problem states that both capacitors have the same plate separation (d) and the four plates are of the same area (meaning the plates for C₁ have area A, and the plates for C₂ also have area A).
– The plates are made of gold and aluminium. These materials are conductors and form the plates; they are not the dielectric material filling the space between the plates. The dielectric material between the plates is presumably the same for both capacitors (usually air or vacuum unless specified otherwise).
– Since A, d, and the dielectric material (and thus its permittivity ε) are the same for both capacitors, their capacitances must be equal.
– The resistivities of gold (ρg) and aluminium (ρa) are properties of the plate materials themselves and do not affect the capacitance value, which is determined by the geometry of the plates and the material *between* them.

The capacitance of a capacitor depends on its physical dimensions (area and separation of plates) and the dielectric properties of the material filling the space between the plates. The conductive material of the plates affects properties like resistance and conductivity, but not the capacitance itself in the standard parallel-plate model.

22. Which one of the following is not a semiconductor?

Which one of the following is not a semiconductor?

Silicon

Germanium

Quartz

Gallium arsenide

This question was previously asked in

UPSC CDS-1 – 2017

Download PDF Attempt Online

The correct answer is C) Quartz.

Semiconductors are materials with electrical conductivity between that of a conductor and an insulator. Silicon (Si) and Germanium (Ge) are elemental semiconductors. Gallium arsenide (GaAs) is a compound semiconductor. Quartz is primarily silicon dioxide (SiO₂), which is an excellent electrical insulator.

Semiconductors have a band gap that is smaller than insulators but larger than conductors, allowing their conductivity to be significantly altered by temperature, doping, and other factors. Insulators like quartz have a large band gap, making it very difficult for electrons to move and conduct electricity.

23. When a piece of pure silicon is doped with aluminium, then

When a piece of pure silicon is doped with aluminium, then

the conductivity of the doped silicon piece will remain the same

the doped silicon piece will become n-type

the doped silicon piece will become p-type

the resistivity of the doped silicon piece will increase

This question was previously asked in

UPSC CDS-1 – 2017

Download PDF Attempt Online

The correct answer is C) the doped silicon piece will become p-type.

Pure silicon is a semiconductor with a valence of four. Aluminium is a Group 13 element and acts as a trivalent impurity (valence of three) when doped into silicon. When a trivalent impurity replaces a silicon atom in the crystal lattice, it creates a ‘hole’ (absence of an electron) in the covalent bond structure. These holes act as positive charge carriers, making the doped semiconductor p-type.

Doping semiconductors with impurities increases their conductivity. Doping with trivalent impurities creates p-type semiconductors (majority carriers are holes), while doping with pentavalent impurities (like Phosphorus or Arsenic from Group 15) creates n-type semiconductors (majority carriers are electrons). Resistivity is the inverse of conductivity, so doping decreases resistivity.