Question

In the circuit shown in the figure, find the current in the 45Ω resistor. 

• A. \(4\,\text{A}\)
• B. \(2.5\,\text{A}\)
• C. \(2\,\text{A}\)
• D. None of these

Hint:

In symmetric resistor networks: • Nodes at the same level have equal potential • Resistors between equipotential points carry no current This greatly simplifies circuit analysis.

Answer 1

The Correct Option is B

Step 1: Observe that the circuit is symmetric about the vertical axis passing through the top node and the bottom junction.
Step 2: Due to symmetry, corresponding nodes on left and right sides are at the same potential. Hence, no current flows through the central 90Ω resistor.
Step 3: Reduce the circuit using series–parallel combinations. The equivalent resistance of each side branch simplifies, and the total equivalent resistance of the circuit is: Rₑq = 72Ω
Step 4: Total current from the 180V source: Itotal = (180)/(72) = 2.5A
Step 5: This current flows through the 45Ω resistor, hence: I₄5Ω = 2.5A