What is the current through 2/3 ohm resistance in the figure shown below;

Asked by tangocharliee | 12th Nov, 2009, 05:04: PM

Expert Answer:

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.

Answered by  | 12th Nov, 2009, 09:02: PM

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