Question

A wire 12m long has a resistance of 1.5. what will be the resistance of 16m of the same wire

Answer 1

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resistance of 12m wire = 1.5 ohm

resistance of 1m wire = 1.5 / 12 = 0.125 ohm

resistance of 16m wire = 2 ohm

Ans. = 2 ohm

Answer 2

Given: Length of wire 1 (l1)= 12m

Resistance of wire 1 (R1) = 1.5Ω

Length of wire 2 (l2) = 16m

To Find: Resistance of wire 2

Solution:

Since the wires are made of the same material they will have the same resistivity(ρ).

ρ1 = ρ2

The area of cross-section will also be same as we are taking 16m from the same wire and the radius will be same

A1 = A2

Resistance of a wire is given as

R = ρ$\frac{l}{A}$

R1 = ρ1$\frac{l1}{A1}$                               .... 1

R2 = ρ2$\frac{l2}{A2}$                             .... 2

On divindig 1 by 2

$\frac{R1}{R2}$  = $\frac{l1}{l2}$                             (Since, ρ1 = ρ2 and A1 = A2)

$\frac{1.5}{R2}$   = $\frac{12}{16}$

R2 = $\frac{24}{12}$

R2 = 2Ω

Therefore, the resistance of the same wire of length 16 m will be 2Ω.