Question

What should be the length of anichrome wire of resistance 4.5ohm, if the length of a similar wire is 60cm and resistance of 2.5ohm

Answer 1

We have to find the length of anichrome wire of resistance 4.5 ohm.

(R1 = 4.5 ohm and l1 = ?)

Length of another similar anichrome wire is 60 cm and it's resistance is 2.5 ohm.

(R2 = 2.5 ohm and l2 = 60 cm)

R = p l/A

We know that, resistance of a wire is directly proportional to it's length i.e. R ∝ l.

As per given condition, there are two wires of anichrome, having resistance 4.5 ohm's and 2.5 ohm and one having length 60 cm & have to find the length of other wire.

We can write it like,

R1 ∝ l1 and R2 ∝ l2

Divide both of them,

R1/R2 = l1/l2

Substitute the known values,

4.5/2.5 = l1/60

1.8 = l1/60

1.8 × 60 = l1

108 = l1

Therefore, the length of the anichrome wire is 108 cm of resistance 4.5ohm.

Answer 2

GiVeN :-

Resistance of a nichrome wire(R₁) = 4.5 Ω

Length of a similar wire (l₂) = 60 cm

Resistance of the similar wire (R₂) = 2.5 Ω

To DeTeRmInE :-

The length of the nichrome wire (l₁).

AcKnOwLeDgEmEnT :-

We know,

$\sf{R=\rho \dfrac{l}{A} }$

Where,

• R is the resistance of the wire.

• ρ is the proportionality constant.

• l is the length of the wire.

• A is the area of cross-section.

So, we get that, R ∝ l and R ∝ 1/A.

SoLuTiOn :-

From the acknowledgement, we obtain :-

→ R₁ ∝ l₁ & R₂ ∝ l₂.

Let R₁ = kl₁ & R₂ = kl₂ where k is a constant.

Dividing the resistances :-

R₁/R₂ = kl₁/kl₂

(k gets cancelled)

4.5/2.5 = l₁/60

⇒l₁ = (4.5 × 60)/2.5

⇒l₁ = 270/2.5

⇒l₁ = 108 cm

Hence, the length of the nichrome wire is 108 cm.