A uniform conductor of resistance R is cut into 20 equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series, the effective resistance of all the pieces is

Step-by-step solution

Resistance of each piece = R 20 Equivalent resistance of 10 such pieces connected in series R₁=10 R 20 = R 2 Similarly, equivalent resistance of 10 such pieces connected in parallel aligned 1 R₂ & = 1 R / 20 + 10 times & = 10 R / 20 = 200 R R₂ & = R 200 aligned Now, R₁ and R₂ are connected in series so total resistance =R₁+R₂ aligned & = R 2 + R 200 & = 100 R+R 200 & = 101 R 200 aligned