JEE Main 2021 · 20 July · evening · Numerical answer · +4 / −0
In the given figure switches S₁ and S₂ are in open condition. The resistance across ab when the switches S₁ and S₂ are closed is _____________ Ω.
Answer and solution
Answer 10
Solution
Physics sir · 3 steps
A closed switch is a plain wire, so it joins the top and bottom rails into one node at each switch.
- Switches become wires. Closing S₁ joins the top and bottom junctions to its left into one point, P. Closing S₂ does the same on the right, giving one point Q. The circuit is now three blocks in series: a to P, P to Q, and Q to b.
- Each block in parallel. Between a and P, the 12 Ω and 6 Ω both join the same two points, so they are in parallel. The same is true for the two 4 Ω between P and Q, and for the 6 Ω and 12 Ω between Q and b.
R_(ab) = (12 × 6)/(12 + 6) + (4 × 4)/(4 + 4) + (6 × 12)/(6 + 12) = 4 + 2 + 4
- So. The resistance across ab with both switches closed is 10 Ω.
The common slip: 11. Working with the switches still open gives two 22 Ω paths in parallel, which is 11, not 10.
The idea to keep. A closed switch has zero resistance, so treat its two ends as one point. Redraw the circuit node by node, and series and parallel groups become easy to see.
Answer from the NTA final answer key. Solution by PrepWiser.