A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the ratio RR′ is
25
When we divide resistance wire in equal ratio the resistance value of each wire is also divided in that ratio. As in this case length of each new wire has reduced but cross section area and resistivity is the same. So the resistance has become 15 of each smaller wire. Now these wires are in parallel. So, the net resistance is
1R′= 5R +5R+5R+5R+5R
R′ = R25
RR′ = 25