JEE MainPhysicsCurrent Electricity
A resistor network is constructed such that a main wire with a single root resistor splits into three parallel branches, each containing one resistor. After these resistors, each of the three branches then splits into three more parallel branches, each containing one resistor (making a total of 9 leaf branches). All 9 leaf branches finally connect to a common return wire. If all the resistors in the network are ident
Correct answer
9
Step-by-step solution
Let the total current entering the network be I and the resistance of each resistor be R . The single root resistor carries the entire current I . The power dissipated in it is: P_ root = I^2 R Due to the symmetry of the network, the current divides equally at each junction. At the first junction, the current splits into three equal parts, so each of the three branches carries a current of I 3 . At the next set of junctions, each I 3 current splits into three equal parts again. Therefore, each of the 9 leaf branche