Question

A uniform wire of resistance 50Ω is cut into 5 equal parts. These parts are now connected in parallel.

Answer 1

The wire is uniform,so here the series connection of resistors should be known first.
here resistance equivalent is 50 ohm.
 
Resistance equivalent  = R + R +R + R + R            (since it is cut into 5 wires )

50 = 5 . R
R = 50 / 5
R = 10 ohm

Now , when these wires are connected in parallel ,
 1 / resistance equivalent = 1 / R + 1 / R + 1 / R + 1 / R + 1 / R   ( since there are 5 wires )

1 / R equivalent = 5 / R
by cross multiplying , we get
 
10 = 5 R equivalent

R equivalent = 10/ 5
   = 2 ohms
Hence , the equivalent resistance of these wires joined in parallel series of connection is 2 ohms