Question

In the above circuit the sum of magnitudes of current (in A) through each resistance is:

Answer 1

0

Answer 2

The circuit consists of three identical parallel sections. Each section has a 2V battery in the top branch and a 2V battery in the bottom branch, with a 1Ω resistor connecting the points between the batteries.

Let the potential at the common left node of a section be $V_X$.

Due to the top 2V battery (positive on left), the potential at the top-right node will be $V_X - 2V$.

Due to the bottom 2V battery (positive on left), the potential at the bottom-right node will also be $V_X - 2V$.

Since both ends of the 1Ω resistor are at the same potential ($V_X - 2V$), the potential difference across the resistor is 0V.

Therefore, the current through each 1Ω resistor is 0A.

The sum of magnitudes of current through each resistance is $0 + 0 + 0 = 0$ A.