Question

In the circuit shown below, all resistances have value of $R = 1\Omega$. Current in the branches shown are $I_1$ & $I_2$ Amperes respectively.

Value of $I_1$ is ____.

Answer 1

$I_1 = 0\text{ A}$

Answer 2

1. Observation using symmetry:

• In the given circuit, each “column” has two identical resistors (all $R=1\,\Omega$).
• The resistor network is balanced; hence the potential at the two nodes connected by the horizontal branch (with current $I_1$) is equal.
• Therefore, by the principle of a balanced Wheatstone bridge, there is no potential difference across the branch carrying $I_1$.

2. Conclusion: $$I_1 = 0\,\text{A}$$

Minimal Explanation

Equal resistors ensure equal potentials at the two nodes in the middle branch. Hence, no current flows there, so $I_1 = 0\text{ A}$.