Question

the resistance of a conductor is 27ohm . if it is cut into three equal parts and connected in parallel, then its total resistance is

Answer 1

Since it is cut into three equal parts, then resistance of each part will become 9 ohm. Now equivalent resistance in parallel will become

1/R = 1/R1 + 1/R2 + 1/R3

1/R = 1/9 +1/9 + 1/9

1/R = 3/9

1/R = 1/3

R = 3 ohm

∴ Equivalent resistance in parallel is 3 ohm

Answer 2

Answer: The equivalent or total resistance of the given connection is 1 ohm.

Explanation:

Resistivity remains constant but resistance gets altered with length and thickness of the wire.

So, when a wire is cut into three equal parts, the resistance also gets divided into three parts and hence now the effective resistance of each part is 3 ohm.

Now, when they are connected in parallel:

The formula for finding equivalent resistance in case of parallel connection:

1/R = 1/r+ 1/r+ 1/r, where R is the equivalent resistance of the parallel connection of the three wires and r represents the resistance of the three wires.

So, 1/R = 1/3 + 1/3 + 1/3

1/R = 1 ohm or R= 1 ohm

Therefore, the equivalent or total resistance is 1 ohm.