The current through 2/3 ohm resistance in the figure shown below is?

Since there is symmetry in the circuit but upside down.

The total current I, splits in currents I₂ and I₄ that go through 2 ohm and 4 ohm respectively.

Due to upside down symmetry the I₂ current will come down 2/3 ohm will go through 2 ohm, similarly I₄ will go up 2/3 ohm will flow through the 4 ohm.

Hence the current through 2/3 ohm is I₂- I₄.

We can write KVL across any two loops and find the currents, for example,

10 - 2I₂ - 4I₄ = 0

10 -4I₄ + (2/3)(I₂-I₄) - 4I₄ = 0

Solving these we find I₂= 7/3 I₄= 4/3,

hence the current through 2/3 ohm resistance is 1 A.

Regards,

Team,

TopperLearning.