JEE Main 2023 · 8 April · evening · Single correct · +4 / −1
The equivalent resistance between A and B as shown in figure is:
- (a) 30 k Ω
- (b) 20 k Ω
- (c) 5 k Ω
- (d) 10 k Ω
Answer and solution
Answer (c) 5 k Ω
Solution
Physics sir · 4 steps
Follow the plain wires first: they merge D with A and C with B, and the rest falls into place.
- Merge joined points. A plain wire has no resistance, so both its ends are at the same potential. The top wire joins A to D, so D is the same node as A. The bottom wire joins C to the right end, so C is the same node as B.
- Relabel each resistor. The first 20 kΩ runs from A to C, that is from A to B. The second 20 kΩ runs from C to D, that is from B to A. The 10 kΩ runs from D to B, that is from A to B.
- All in parallel. Every resistor now connects A directly to B, so all three are in parallel.
1/R_(AB) = 1/20 + 1/20 + 1/10 = 4/20 kΩ⁻¹
- So. R_(AB) = 20/4 = 5 kΩ, which is option (c).
The idea to keep. Before combining anything, give every junction joined by a bare wire the same label. Resistors that look like they are in series often turn out to sit between the same two nodes.
Answer from the NTA final answer key. Solution by PrepWiser.