For the resistive ladder circuit shown in the figure (9 V source, top branch 3 Ω, 2 Ω, 2 Ω; bottom branch three 2 Ω resistors; vertical branches 8 Ω, 8 Ω, 4 Ω), the current through the 4 Ω resistor is 1/K ampere. Find K.
Physics · Mixed Chapter
JEE Mains

Question

For the resistive ladder circuit shown in the figure (9 V source, top branch 3 Ω, 2 Ω, 2 Ω; bottom branch three 2 Ω resistors; vertical branches 8 Ω, 8 Ω, 4 Ω), the current through the 4 Ω resistor is 1/K ampere. Find K.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Explanation: Reduce the ladder from the right: rightmost path 2+4+2=8 Ω in parallel with its adjacent 8 Ω branch gives 4 Ω. Include the next top/bottom 2 Ω resistors: 2+4+2=8 Ω, in parallel with the first 8 Ω gives 4 Ω. Source sees 3+4+2=9 Ω and supplies 1 A. Each equal parallel split halves current, so the far-right 4 Ω carries 1/4 A. K=4.