Question

A wire having 24 cm of length and 12 ohm resistance is used to make a square. What will be the effective
resistance between the diagonally opposite points of this square?
(A) 6 ohm
(B) 3 ohm
(C) 3/2 ohm
(D) 12 ohm​

Answer 1

Answer:

It's correct answer is option

:- (D)- 12 ohm

Answer 2

Answer:

Option (A) 6 ohm

Explanation:

Given that:

A wire having 24 cm of length and 12 ohm resistance is used to make a square.

24 cm of length is equivalent with 12 ohm resistance.

So we get the resistance/unit length;

$ρ = \frac{12}{24} \: ohm \: .{cm}^{ - 1} \\ ρ= 0.5 \: ohm \: .{cm}^{ - 1}$

Let the side of square = a cm

The perimeter of the square = 4a cm = 24 cm

So, the side of square;

$4a = 24 \: cm \\ a = \frac{24}{4} \: cm \\ a = 6 \: cm$

The Distance between any two Diagonally Opposite points = Length of two sides

So, Distance between any two Diagonally Opposite points = 2a cm = 12 cm

So, Resistance between any two Diagonally Opposite points ;

$resistane(r) = 12 \times ρ \: ohm \\ r = 12 \times 0.5 \: ohm \\ r = 6 \: ohm$

So the resistance is 6 ohm.