Question

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a wire of given material having length L and area of cross section A has a resistance of 10 ohm.
what would be the resistance of another wire of the same material having length L/4 and area of cross section 2.5A?
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answer only if you know.
thanks :^)

Answer 1

For wire one

l = L
a = A
R = 10 Ω

R = ρ l / a

10 = ρ L/A

ρ = 10 A / L


For wire 2

l = L/4
a = 2.5 A
ρ = 10A/L


R = ρ l/a

= 10 A / L × L / 4 × 2.5 A

= 1

So the resistance is 1 Ω .


HOPE IT IS MOST HELPFUL!!!!!!!!!!!!!

Answer 2

RESISTANCE OF THE SECOND WIRE IS 1 OHM.

Given:

• First wire has length L and area A and resistance of 10 ohm.

• Second wire has length L/4 and area 2.5 A.

To find:

• Resistance of second wire ?

Calculation:

For the first wire, we can say :

$R = \rho \times \dfrac{length}{area}$

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

$\implies \rho \times \dfrac{L}{A} = 10$

Now, for the second wire :

• Since both the wires are made of the same material, the value of $\rho$ will be same.

$R2= \rho \times \dfrac{length}{area}$

$\implies R2 = \rho \times \dfrac{( \frac{L}{4})}{2.5(A)}$

$\implies R2 = \rho \times \dfrac{L}{(2.5 \times 4)A}$

$\implies R2 = \rho \times \dfrac{L}{10A}$

$\implies R2 = \dfrac{1}{10} \times (\rho \times \dfrac{L}{A})$

$\implies R2 = \dfrac{1}{10} \times 10$

$\implies R2 = 1 \: ohm$

So, resistance of the second wire is 1 ohm.