GATE 2026 IN Q.28: solution and answer

Official answer: CSource: Official answer key, GATE 2026 IN (IIT Guwahati)

1. Above threshold, the piece-wise linear light-current characteristic is $P={\eta }_s(I-I_{th})$, and the output is zero below $I_{th}$.

2. Given: ${\eta }_s=0.5\text{W/A}$, $I=100\text{mA}$, $P=30\text{mW}$.

3. $P$ is non-zero, so the diode is operating above threshold and the linear relation applies.

4. The current above threshold is $$I-I_{th}=\frac{P}{{\eta }_s}=\frac{30\times 10^{-3}\text{W}}{0.5\text{W/A}}=60\text{mA}$$

5. The threshold current is $$I_{th}=100\text{mA}-60\text{mA}=40\text{mA}$$

6. This is option (C).