JEE Main 2023 · 24 January · evening · Single correct · +4 / −1
The logic gate equivalent to the given circuit diagram is :
- (a) NOR
- (b) OR
- (c) NAND
- (d) AND
Answer and solution
Answer (c) NAND
Solution
Physics sir · 4 steps
The switches sit across the bulb, so closing both shorts it out. Off only for 1, 1: that is NAND.
- Read the circuit. The bulb and the two switches A₁, B₁ connect the same two points, so the switch path is in parallel with the bulb. The resistor below them goes to ground and limits the current.
- Any switch open. If even one switch is open, the switch path is broken. All the current goes through the bulb, so it glows and Y = 1.
- Both switches closed. Now the switch path is a plain wire with almost zero resistance across the bulb. The current bypasses the bulb, so it does not glow and Y = 0. The resistor stops this from shorting the supply.
A₁ B₁ Switch path Bulb Y 0 0 broken glows, 1 0 1 broken glows, 1 1 0 broken glows, 1 1 1 shorts the bulb off, 0 - So. The output is 0 only when both inputs are 1, so Y = A · B̅. The circuit is a NAND gate, option (c).
The idea to keep. Check where the switches are relative to the bulb. Switches in series with the bulb give AND, but switches in series placed across the bulb short it out and invert that to NAND.
Answer from the NTA final answer key. Solution by PrepWiser.