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

resistance of the wire=r
<-------------- r----------------->
•________•__________•
A r/2 B r/2 C
This wire is connected in parallel.
let the current flowing in this wire =I
p.d across the wire =v
Let the current flowing through the given resistance be I and i
From ohm's law, V=IR
or, I=V/R
so, V=Ir/2
or,I=V/r/2
and V=ir/2
or, i=V/r/2
Total current in the wire is ,
I=i+I
V/R=V/r/2 + V/r/2
V/R=V(2/r+2/r)
1/R=(2+2)/r
1/R=4/r.....................1)
Equation 1 give the total resistance of the wire in parallel connection.
I HOPE THIS WILL HELP YOU......

Answer 2

Answer: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.  

 

When connected in parallel  

1/Req = 1/R1 + 1/R2 + 1/R3

1/Req = 3/R + 3/R + 3/R

1/Req = 9/R

Req = R/9