Question

A wire has a resistance of 16 ohms. It is melted and drawn into a wire of half of its original length. What is the resistance of the new wire?
1. 4 ohms
2. 32 ohms
3. 16 ohms
4. 8 ohms

Answer 1

Correct Answer - Option 1 : 4 ohms

CONCEPT:

• Resistance (R): The resistance offered to the flow of current is known as the resistance.
  • The SI unit of resistance is the ohm (Ω).
• Mathematically resistance can be written as:

\(⇒R = \frac{{\rho l}}{A}\)

Where R = resistance, l = length, A = area of cross-section and ρ = resistivity

CALCULATION:

Given that:

L2 = L1/2

So L1/L2 = 2

• As we know that the resistance of the wire is,

\(⇒ R = \frac{{\rho L}}{A}\)

• When the wire is melted and its length halved then its diameter will increase automatically. But the volume of the wire will be the same.

∴ The volume of original wire = volume of new wire

⇒ A1L1 = A2L2

⇒ A₁/A₂ = L₂/L₁ = 1/2

• The resistance of the wire in 1st case:

\(⇒{R_1} = R = \frac{{\rho {l_1}}}{{{A_1}}} = 16\; \Omega \)      

• The resistance of the wire in 2nd case

\(⇒{R_2} = \frac{{\rho {L_2}}}{{{A_2}}} = \frac{\rho (L_1/2)}{2A_1}=\frac{{\rho {L_1}}}{{{4A_1}}}=\frac{R_1}{4}=16/4 = 4 \; \Omega \)