Question

A wire of length 80cm has resistance of 3.5ohm. The length of similar wire of resistance 10.5ohm is​

Answer 1

Answer:

Correct answer is 7.5ohm...

Explanation:

In the question, it is given that the resistance of one meter wire is 3 ohms. So the resistance of 1.5 meters of the same wire is given as

1

3×5

=15ohms.

The resistance of a resistor is given by the formula R=ρ

A

L

where ρ is the resistivity of the material the resistor is made of, l is the length of the resistor and A is the cross-sectional area.

Let the resistance of the wire is initially equal to R. R=ρ

A

L

.

When the area of cross-section of the wire is doubled and so the resistance of the wire is given as R

′

=ρ

2(A)

L

.

The new resistance is R

′

=

2

R

.

Hence, the changed resistance of the wire is 15/2=7.5 ohms.

Hope it's helpful...!!!

Answer 2

Answer:

The length of a similar wire with a resistance of 10.5Ω is 2.4m.

Explanation:

Resistance of a substance is the property by which it offers opposition to the flow of current.

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.i.e.

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

$R=\rho \frac{L}{A}$               (1)

R=resistance of the wire

ρ=resistivity of the wire=it remains constant for a given material of the wire

L=length of the wire

A=Cross sectional area of the wire

The values given in the question are,

L₁=80cm=0.8m

R₁=3.5Ω

R₂=10.5Ω

By putting the value of R₁ and L₁ in equation (1) we get;

$3.5=\rho \frac{0.8}{A}$

$\frac{\rho}{A}=\frac{3.5}{0.8}=\frac{35}{8}$          (2)

For L₂ we will substitute R₂ and equation (2) in equation (1);

$10.5=\frac{35}{8} \times L_2$

$L_2=2.4m$

Hence, the length of the wire with a resistance of 10.5Ω is 2.4m.