Question

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?

Answer 1

Concept: Resistance of a wire is directly proportional to its length. \[ R \propto l \] If length is doubled → Resistance doubles. From Ohm’s law, \[ I = \frac{V}{R} \] So current is inversely proportional to resistance. Result: If resistance doubles, current becomes half. \[ \text{New current} = \frac{X}{2} \]

Answer 2

Step 1: Relation between resistance and area.
Resistance of a conductor is given by:
R = ρL/A
This shows that resistance is inversely proportional to the area of cross-section.
R ∝ 1/A

Step 2: Effect of doubling the area.
If the area of cross-section is doubled, then:
New resistance R' = R/2
Thus, resistance becomes half of its original value.

Step 3: Apply Ohm’s law.
According to Ohm’s law:
I = V/R
If resistance decreases and voltage remains constant, current increases.

Step 4: Calculate new current.
Since the new resistance is R/2:
I' = V / (R/2)
I' = 2V/R
I' = 2I

Result:
If resistance becomes half, the current becomes double.
New current = 2X

Answer 3

Step 1: Definition of resistivity.
Resistivity is a fundamental property of a material that measures how strongly the material opposes the flow of electric current.
It depends only on the nature of the material and temperature, not on its shape or size.

Step 2: Formula of resistivity.
Resistivity (ρ) is given by the relation:
ρ = RA / l
where R is resistance, A is cross-sectional area, and l is the length of the conductor.

Step 3: SI unit of resistivity.
The SI unit of resistivity is ohm metre (Ω m).

Step 4: Comparison between alloys and pure metals.
Alloys generally have higher resistivity than their constituent pure metals.
This happens because the presence of different atoms and irregular structure in alloys obstructs the flow of electrons.
The increased scattering of electrons leads to higher resistance and hence higher resistivity.

Answer 4

(i) Why tungsten is used for making lamp filaments:

Step 1: High melting point.
Tungsten has an extremely high melting point (about 3400°C).
Because of this, it can withstand very high temperatures without melting.

Step 2: High resistivity.
Tungsten has high resistivity, so when electric current passes through it, a large amount of heat is produced.
This high temperature makes it glow and emit light.

Step 3: Ability to emit light.
When heated to very high temperatures, tungsten emits bright white light.
This makes it suitable for use as a filament in electric bulbs.

Conclusion:
Tungsten is used for lamp filaments because of its very high melting point, high resistivity, and ability to glow without melting.

(ii) Why conductors of bread-toasters are made of an alloy:

Step 1: Higher resistivity.
Alloys have higher resistivity than pure metals.
Higher resistivity produces more heat when current passes through them.

Step 2: Resistance to oxidation.
Alloys do not oxidize or burn easily at high temperatures.
This increases their durability.

Step 3: Long-lasting property.
Alloys can withstand repeated heating without melting or breaking easily.

Conclusion:
Conductors of bread-toasters are made of alloys because they produce more heat, resist oxidation at high temperatures, and last longer than pure metals.

Answer 5

(i) Why tungsten is used for making lamp filaments:

Tungsten has a very high melting point (around 3400°C), so it can withstand extremely high temperatures without melting.
It has high resistivity, which allows it to produce a large amount of heat when electric current passes through it.
At very high temperatures, tungsten emits bright light without melting.
These properties make it ideal for use in electric lamp filaments.

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

Alloys have higher resistivity than pure metals, so they produce more heat when current flows through them.
They do not oxidize or burn easily at high temperatures.
They can withstand repeated heating and cooling without breaking.
Therefore, alloys are more durable and suitable for use in heating elements of bread-toasters.