Question

A uniform wire of resistance R is cut into two equal pieces and these pieces are joined in parallel . what is the resistance of the combination​

Answer 1

Given that, a uniform wire of resistance R is cut into two equal pieces and these pieces are joined in parallel.

Assume a wire having resistance R which is cut perpendicular into two equal pieces, which are later joined together in parallel.

We have to find the resistance of the company combination. (Means, Rp).

For series combination: Rs = R1 + R2 and For parallel combination: Rp = 1/R1 + 1/R2

In the above question we are talking about parallel combination. So, the formula used here is 1/Rp = 1/R + 1/R2.

Also, we can say that, R1 = R2 = R/2.

1/Rp = 1/R1 + 1/R2

1/Rp = 1/(R/2) + 1/(R/2)

1/Rp = 2/R + 2/R

1/Rp = (2 + 2)/R

1/Rp = 4/R

→ Rp = R/4

Therefore, the resistance of the combination is R/4 ohm.