Question

Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length ‘l’ in the circuit and after plugging the key, noted current in the ammeter. Ayesha put nichrome wire of same thickness but twice the length i.e. ‘2l’ in the circuit and after plugging the key, noted current in the ammeter. Samridhi took copper wire of length ‘l’ and same thickness in the circuit and after plugging the key, noted current in the ammeter.

(a) If the ammeter reading is X ampere with nichrome wire of length ‘l’, then what will be the ammeter reading if the length of nichrome wire is doubled with same area of cross-section?

(b) What happens to the ammeter reading if the area of cross-section of nichrome wire is doubled, keeping the length of wire ‘l’ the same?

(c) Define ‘resistivity’. Write its SI unit. Compare the resistivity of an alloy with its constituents metals.

OR

(c) Give reason:

(i) Tungsten is used almost exclusively for making the filament of electric lamps.

(ii) Conductors of bread-toasters are made of an alloy rather than a pure metal.

Answer 1

(a) Resistance of a wire is directly proportional to its length.

R ∝ l

If the length is doubled, the resistance becomes double.

From Ohm’s law,

I = `V/R`

So current is inversely proportional to resistance.

Hence, if resistance doubles, the current becomes half.

New current = `X/2`

(b) Resistance is inversely proportional to the area of cross-section.

R ∝ `1/A`

If the area is doubled, the resistance becomes half.

From Ohm’s law,

I = `V/R`

So current increases when resistance decreases.

If resistance becomes half, the current doubles.

New current = 2X

Resistivity is a property of a material that measures how strongly it opposes the flow of electric current.

ρ = `(R A)/l`

The SI unit is Ohm meter (Ω m).

Alloys generally have higher resistivity than their constituent pure metals. This is because impurities and irregular structure increase resistance to electron flow.

OR

(c) (i) Tungsten has a very high melting point and can endure higher temperatures without melting. It exhibits high resistance and emits light when heated, making it suitable for lamp filaments.

(c) (ii) Alloys have a higher resistance and do not oxidise easily when they get hot. They last longer and make more heat than pure metals.