Which one of the following physical quantities does NOT affect the resistance of a cylindrical resistor ?
- (a)The current through it
- (b)Its length
- (c)The resistivity of the material used in the resistor
- (d)The area of cross-section of the cylinder
Correct — A, The current through it. The resistance of a uniform cylindrical conductor is R = ρL/A, where ρ is the resistivity of the material, L the length and A the area of cross-section. Current does not appear anywhere in that expression. For an ohmic conductor the ratio of potential difference to current is a constant, which is precisely the statement that resistance does not depend on how much current is flowing; push twice the current through and the potential difference across it simply doubles. Resistance is a property of the object — what it is made of and what shape it has — and not of the electrical traffic passing through it at that instant.
- (b)Its length — Resistance is directly proportional to length. A longer conductor makes the drifting electrons travel further against more collisions, so a wire twice as long has twice the resistance.
- (c)The resistivity of the material used in the resistor — Resistivity is the material's own contribution and it multiplies straight into the formula. Nichrome has a far higher resistivity than copper, which is exactly why heating elements are wound from nichrome and connecting leads are made of copper.
- (d)The area of cross-section of the cylinder — Resistance is inversely proportional to the area of cross-section. A thicker wire offers a wider path, so doubling the area halves the resistance — which is why heavy-current circuits are wired in thick cable.
Resistance measures how strongly an object opposes the flow of charge, and R = ρL/A separates that opposition into a material part and a geometrical part. Resistivity ρ belongs to the substance and is quoted in ohm metre; it does not change when you cut the wire or stretch it. Length and cross-section belong to the specimen. Temperature is the one further influence that matters in practice, since the resistivity of a metal rises as it gets hotter — which is why the resistance of a filament lamp measured cold is much lower than its resistance when glowing.
The word NOT is the hinge of this question, so read it twice. Three of the options are the three symbols in R = ρL/A, and the fourth is the quantity the formula deliberately leaves out. There is one honest refinement worth carrying: at large currents a resistor heats up, and that temperature rise does change its resistance. That is a thermal effect working through temperature, not a direct dependence on current, and for an ohmic resistor at steady temperature — which is what the question intends — resistance is independent of current.
- For a uniform conductor, R = ρL/A — resistance is proportional to length and inversely proportional to area of cross-section.
- The SI unit of resistivity is the ohm metre, while resistance is measured in ohm.
- Ohm's law states that for a conductor at constant temperature the ratio of potential difference to current is constant.
- The resistivity of a metal rises with temperature, whereas that of a semiconductor falls.
- Reading the question without the NOT and choosing a quantity that does affect resistance.
- Confusing resistance with resistivity — cutting a wire in half halves the resistance but leaves the resistivity untouched.
- Forgetting that heating changes resistance, and then over-correcting into thinking current itself appears in the formula.
NDA asks what resistance depends on, or gives a wire that is cut, stretched or recombined and asks for the new resistance.
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 same formula probed from the resistivity side, separating what belongs to the material from what belongs to the specimen.
Which one of the following correctly represents the SI unit of resistivity?
- (a) Ω
- (b) Ω/m
- (c) Ω cm
- (d) Ω m
Answer(d) Ω m
The unit that falls straight out of the same relation, and a quick check that you have the formula the right way up.
- practice — not a real PYQ
A wire of resistance R is cut into two equal halves and the two halves are joined in parallel. The resistance of the combination is
- (a)R
- (b)R/2
- (c)R/4
- (d)2R
Answer(c) R/4 — each half has resistance R/2, and two equal resistances in parallel give half of that.
- practice — not a real PYQ
The resistivity of a metallic wire depends on
- (a)its length
- (b)its area of cross-section
- (c)the material and the temperature
- (d)the current flowing through it
Answer(c) the material and the temperature — resistivity is a property of the substance and changes with temperature, but not with the dimensions of the specimen.