Q 12-14-072JEE MainJEE Main 2024 (8 Apr, Shift 2)Medium
A potential divider circuit is connected with a dc source of $20\ \text{V}$, a light emitting diode of glow-in voltage $1.8\ \text{V}$ and a Zener diode of breakdown voltage $3.2\ \text{V}$. The length (PR) of the resistive wire is $20\ \text{cm}$. The minimum length of PQ to just glow the LED is ______ cm.
Numerical value type. Enter your answer.
Answer: 5
The LED glows only when the voltage across PQ is enough to forward bias the LED and drive the Zener into breakdown:
$$V_{PQ} = 1.8 + 3.2 = 5\ \text{V}$$
The wire has a potential gradient of $\dfrac{20\ \text{V}}{20\ \text{cm}} = 1\ \text{V/cm}$, so $PQ = 5\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics