Find the current in each resistor 

 

In the given circuit R1 and R4 are in series .

Hence Equivalent resistance R7 = 4Ω replaces resistors R1 and R4 in the circuit shown above.

 

Similarly , in the given circuit, R3 and R5 are in parallel. 

Hence Equivalent resistance R6 = 4Ω replaces resistors R3 and R5 in the circuit shown above. 

 

Let us assume the current distribution as shown in figure.

 

If we apply Kirchoff's voltage law to the loop ABEFA , we get

 

4 ₁ + 4 ₃ + 2 = 2   or  ₁ = - ₃   ............................ (1)

If we apply Kirchoff's voltage law to the loop BCDEB , we get 

 

4 ₁ + 4 ₂ + 2 = 2   or  ₁ = - ₂  ...........................(2) 

At node B , if we apply Kirchoff's current law , we get  ₁ = ₂ + ₃  ...............................(3)

From equations (1), (2) and (3) , we get , ₁ = ₂  = ₃ = 0

Hence current through all resistors is zero