Question

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

Answer 1

Answer:

R' = R/9

Explanation:

Resistance of a wire is directly proportional to its length. Hence, a uniform wire of resistance R is cut into 3 smaller pieces, the resistance of each of the smaller wires would be R/3.  

 Let the new resistance be R'.

When connected in parallel  

1/R'(eq) = 1/R1 + 1/R2 + 1/R3

1/R'(eq) = 3/R + 3/R + 3/R

1/R'(eq) = 9/R

R'(eq) = R/9

Answer 2

Answer:

R' = R/9

Explanation:

Resistance of a wire is directly proportional to its length. Hence, a uniform wire of resistance R is cut into 3 smaller pieces, the resistance of each of the smaller wires would be R/3.  

Let the new resistance be R'.

When connected in parallel  

1/R'(eq) = 1/R1 + 1/R2 + 1/R3

1/R'(eq) = 3/R + 3/R + 3/R

1/R'(eq) = 9/R

R'(eq) = R/9