Question

Two copper wires have the same cross-sectional area but have different lengths. Wire X has a length L
and wire Y has a length 2L. The ratio between the resistance of wire Y and wire X is:

Answer 1

Answer:

The ratio between the resistance of wire Y to wire X is 2 : 1.

Explanation:

Given,

The area of two copper wires X, and Y are same (A)

The length of wire X (Lₓ) = L

The length of wire Y ($L_Y$) = 2L

To find,

The ratio between the resistances of wire Y to X

Calculation,

Let the resistance of wire 'X' be Rₓ

Let the resistance of wire 'Y' be $R_Y$

We know that the resistance of wire (R) is directly proportional to the length of the wire(L) and inversely proportional to the cross-sectional area of the wire(A).

i.e. $R\propto \frac{l}{A}$

$\implies \frac{R_X}{R_Y} = \frac{L_X}{L_Y}\times \frac{A_Y}{A_X}$

But $A_X = A_Y = A, L_X = L, L_Y = 2L$

$\implies \frac{R_X}{R_Y} = \frac{L}{2L}\times \frac{A}{A}$

$\implies \frac{R_X}{R_Y} = \frac{1}{2}$

⇒ $R_Y$/Rₓ = 2 : 1

Therefore, the ratio between the resistance of wire Y to wire X is 2 : 1.

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Answer 2

Answer:

The ratio between the resistance of wire Y and wire X is 2:1.

Explanation:

• A copper wire is defined as the electrical conductor that is categories into electrical wiring.
• It is used in power generation, power transmission, and telecommunications.

• Other uses of copper wire:

1) It is a good conductor of the electricity.

2) It can withstand temperatures from lower level to extreme high voltage.

3) They are affordable because it is less expensive when compared to other metals.

4) It is used in air conditioners and kitchen appliances.

Given that:

The Two copper wires have the same cross-sectional area but have different lengths.

The Wire X has a length L

and wire Y has a length 2L.

To find:

To calculate the ratio between the resistance of wire Y and wire X is: =?

Solution:

Let us consider the resistance of

Wire x to be $R_{x}$

Wire y to be $R_{y}$.

Lets us consider, the definition of resistance,

The resistance of the wire (R ) will be directly propotinao to the length of the wire ( L) and it is inversely proportional to cross-sectional area of a wire (A).

Let us take,

R directly proportional to 1/A

$R_{x}$/ $R_{y}$ = $L_{x}$ /$L_{y}$ * $A_{y}$/ $A_{x}$

Here, Ax = Ay is A

Lx= L & Ly = 2L

$R_{y} / R_{x}$ = $L/ 2L$* $A / A$

$R_{x} / R_{y}$ = ½

$R_{y} / R_{x}$ = 2:1

Hence, the ratio between the resistance of the wire Y to wire X is 2:1

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