What is the correct sequence of resistivity of silver, nichrome and glass at room temperature?
- (a)Silver < Nichrome < Glass
- (b)Glass < Nichrome < Silver
- (c)Silver < Glass < Nichrome
- (d)Nichrome < Silver < Glass
Correct — A, Silver < Nichrome < Glass. The three materials are one from each of the three families, and the ordering follows from the family alone. Silver is the best conductor of all the metals, with a resistivity of about 1·6 × 10⁻⁸ ohm-metre at room temperature. Nichrome is a nickel–chromium alloy, and alloying deliberately spoils the conduction — its resistivity is around 110 × 10⁻⁸ ohm-metre, roughly seventy times silver's, which is exactly why heating elements in irons, toasters and geysers are wound from nichrome rather than from a good conductor. Glass is an insulator, sitting somewhere between 10¹¹ and 10¹⁵ ohm-metre. The gap from either metal to glass is about nineteen orders of magnitude, so once the materials are sorted into metal, alloy and insulator the sequence cannot come out any other way.
- (b)Glass < Nichrome < Silver — The whole sequence run backwards. It puts an insulator at the bottom and the best metallic conductor at the top, which would make glass the natural material for wiring and silver the natural material for a heating coil.
- (c)Silver < Glass < Nichrome — Slips glass in between the two metals. Nothing sits between a metal and an insulator on this scale — glass is about 10¹³ times more resistive than nichrome, not somewhere below it.
- (d)Nichrome < Silver < Glass — Gets the insulator right but swaps the two metals. If nichrome really conducted better than silver, it would be a poor choice for a heating element, since heating relies on the element opposing the current.
Resistivity is the property of the material itself, the constant in R = ρl/A that survives when the shape of the specimen is divided out. Change the length or the thickness of a wire and the resistance changes, but the resistivity does not. It does depend on the material and on the temperature, which is why the question bothers to say 'at room temperature'. Broadly, metals sit near 10⁻⁸ ohm-metre, semiconductors occupy the wide middle ground, and insulators run to 10¹⁶ ohm-metre and beyond. Metals and alloys grow more resistive as they are heated, whereas semiconductors and most insulators grow less so.
No numbers are needed here, only a classification. Ask what each substance is — a pure metal, an alloy of metals, an insulator — and the ranking writes itself. The one piece of specific knowledge that helps is why an alloy is more resistive than its parent metals: a regular lattice of identical atoms scatters conduction electrons the least, and mixing in a second kind of atom disrupts that regularity. Nichrome adds a second useful property on top of the high resistivity — it does not oxidise away at red heat — and the two together are why it is the standard heating-element material.
- At about 20 °C, silver has a resistivity of roughly 1·59 × 10⁻⁸ ohm-metre, the lowest of any metal.
- Nichrome, a nickel–chromium alloy, comes in near 110 × 10⁻⁸ ohm-metre — about seventy times silver's.
- Glass runs from about 10¹¹ to 10¹⁵ ohm-metre, so it is roughly nineteen orders of magnitude above the metals.
- Resistivity depends on the material and its temperature, not on the length or cross-section of the specimen.
- Metals become more resistive when heated; semiconductors and insulators become less resistive.
- Confusing resistivity with resistance and letting the length or thickness of a specimen change the answer.
- Assuming an alloy must conduct at least as well as its constituent metals.
- Forgetting the temperature qualifier, which matters because heating moves metals and insulators in opposite directions.
As an ordering of materials like this one, as a definition-of-units item, or as a trap asking whether resistivity changes when a wire is cut or stretched.
Which of the following statements are correct about the electrical resistance and resistivity of a wire ? 1. Both quantities depend on the area of cross-section of the wire 2. Both depend on the temperature 3. Resistance of the wire is directly proportional to the resistivity of the wire 4. Resistivity of the wire is directly proportional to the length of the wire Select the correct answer using the code given below :
- (a) 1 and 2
- (b) 1 and 3
- (c) 2 and 3
- (d) 2 and 4
Answer(c) 2 and 3
The distinction stated as a set of claims to be sorted. Temperature moves both quantities and resistance follows resistivity, but neither the length nor the cross-section of a wire can touch the resistivity of the metal it is made of.
CDS_GK_2021_I_Q1032021We are given three copper wires of different lengths and different areas of cross-section. Which one of the following would have highest resistivity?
- (a) Copper wire of 50 cm length and 1 mm diameter
- (b) Copper wire of 25 cm length and 0·5 mm diameter
- (c) Copper wire of 10 cm length and 2·0 mm diameter
- (d) All the wires would have same resistivity
Answer(d) All the wires would have same resistivity
The other half of the same idea. Here three different materials are ranked; there three different shapes of one material are ranked, and the point is that shape does not enter — resistivity belongs to the substance.
- practice — not a real PYQ
A copper wire is stretched so that its length doubles and its cross-sectional area halves. Which one of the following is true?
- (a)Its resistance and its resistivity both double
- (b)Its resistance becomes four times, and its resistivity is unchanged
- (c)Its resistance is unchanged, and its resistivity becomes four times
- (d)Both its resistance and its resistivity are unchanged
Answer(b) Its resistance becomes four times, and its resistivity is unchanged — R = ρl/A doubles for the length and doubles again for the halved area, while ρ is a property of copper itself.
- practice — not a real PYQ
The material most suitable for the heating element of an electric iron should have
- (a)very low resistivity and a low melting point
- (b)high resistivity and a high melting point
- (c)very low resistivity and a high melting point
- (d)high resistivity and a low melting point
Answer(b) high resistivity and a high melting point — the element must oppose the current enough to dissipate heat, and survive being kept red hot. Nichrome fits both requirements.