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

Options

A. R
B. `(R )/(2)`
C. `(101R)/(200)`
D. `(201R)/(200)`

Answer

B

Explanation

`(R_1)/(R_2)= ((l_1)/(l_2))^2`
Rightarrow `(R_1)/(R_2)= ((i_1)/(2l_1))^2` `(therefore l_2=2l_1)`
Rightarrow `(R_1)/(R_2) = (1)/(4)`
Rightarrow `R_2 = 4(3) = 12Omega`
The conductor is bent in the form of equilateral traingle
`R_1= R_2 =R_3 =(12)/(3) = 4Omega`
`R_1` and`R_2` are in series , `R'= R_1+R_2 = 8 Omega`
R' and `R_3` are in parellel,
`R(eff) = (R'R_3)/(R'+R_3) = ((8)xx(4))/(8+4) = (32)/(12) =(8)/(3) Omega`