Question

You have two wires of same length and same thickness.one is made of material A(resistivity = 1.6*10^-8) and other is made of material D(resistivity = 96*10^-8).If resistance of wire made of A is 2 ohm.what is the resistance of other wire​

Answer 1

Answer:

The resistance of other wire is 120 ohms.

Explanation:

Resistivity of material A, \rho_1=1.6\times 10^{-8}\ \Omega-mρ

1

=1.6×10

−8

Ω−m

Resistivity of material B, \rho_2=96\times 10^{-8}\ \Omega-mρ

2

=96×10

−8

Ω−m

The resistance of wire A, R_1=2\ \OmegaR

1

=2 Ω

We need to find the resistance of wire B. It can be calculated using formula of resistance in terms of resistivity as :

R=\rho\dfrac{l}{A}R=ρ

A

l

Since, two wires of same length and same thickness. So,

For two wires,

\dfrac{R_1}{R_2}=\dfrac{\rho_1}{\rho_2}

R

2

R

1

=

ρ

2

ρ

1

\dfrac{R_1}{R_2}=\dfrac{\rho_1}{\rho_2}

R

2

R

1

=

ρ

2

ρ

1

R_2=\dfrac{R_1\rho_2}{\rho_1}R

2

=

ρ

1

R

1

ρ

2

R_2=\dfrac{2\times 96\times 10^{-8}}{1.6\times 10^{-8}}R

2

=

1.6×10

−8

2×96×10

−8

R_2=120\ \OmegaR

2

=120 Ω

So, the resistance of other wire is 120 ohms. Hence, this is the required solution.