Question

A wire that has resistance R is cut into two equal piece. The two parts are joined in parallel. What is the resistance of the combination?

Answer 1

Let a wire be long enough with resistance R.

When it's cut in two equal pieces then we get, R1 and R2.

Here, one should remember that:

• R1 = R2

→ 1/Rp = 1/R1 + 1/R2

→ 1/Rp = 1/R1 + 1/R1

→ 1/Rp = 2/R1

→ Rp = R1/2

Hence whatever resistance of Rp is, will be equal to half of it's each part resistance.

The new resistance formed is half of R1.