# CBSE Class 12-science Answered

**give me the answer**

Let us assume a potential difference V is applied between A and B as shown in figure.

Let i be the current drawn by the given resistor network .

At point C , input current i is split into i_{1 }and i_{2} . By symmetry at H , i_{1 }and i_{2} combine to give i .

At point D , current i_{2} is split into i_{3 }and i_{4} . By symmetry at G , i_{3 }and i_{4} combine to give i_{2} .

At point E , current i_{1} and i_{3} combine to give current i_{5.} By symmetry at F , current i_{5} is split into i_{1} and i_{3} .

By applying Kirchoff's voltage law to the loop CIJEC , we get

; Hence we get , ............................. (1)

Similarly by applying Kirchoff's voltage law to the loop DEFGMND , we get

..............................(2)

By applying Kirchoff's voltage law to ACDEFGHBOPA , we get

Hence we get from above expression ,

............................(3)

Using eqn.(1) , we get from above equation as

............................(4)

By substituting i_{5 }in eqn.(2) , we get

.........................(5)

At junction E , by applying Kirchoff's current law , we get

Using eqn.(4) and (5) , we get current i_{1} from above expression as

By substituting i_{3} and i_{5 }in eqn.(3)** , **we get** **

Hence total current drawn by given resistor network is

Hence the effective resistance between points A and B is (r/2)