Question

find the ratio of the resistance of the three wires of same material whose lengths are L,L/3 AND 3L

Answer 1

Answer :-

In solving this question we will be using

$R \propto \dfrac{L}{A}$

$R = \rho \dfrac{L}{A}$

Where

▪️R :- Resistance

▪️L :- Length

▪️A :- Area of cross section

As given

▪️ρ :- Resistivity of material

Let resistance be equal to length L and "A" be constant

For length L

$R_1 = \rho \dfrac{L}{A}$

For length L/3

$R_2 = \rho \dfrac{\dfrac{L}{3}}{A}$

$R_2 = \rho \dfrac{L}{3A}$

For length = 3L

$R_3 = \rho \dfrac{3L}{A}$

Now Ratio

$R_1 : R_2 : R_3$

$= 1 : \dfrac{1}{3} : 3$

$= 3 : 1 : 9$