GATE 2017 EC (EC2) – Question 47
For a particular incident-light intensity on a silicon pn-junction solar cell, photocurrent density $J_L=2.5$ mA/cm² and open-circuit voltage $V_{OC}=0.451$ V. The thermal voltage is $V_T=25$ mV. If the incident-light intensity is increased by 20 times at unchanged temperature, the new $V_{OC}$ (in volts) is ________.
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Correct answer: 0.51 to 0.62
Explanation
At open circuit the photocurrent is balanced by the diode current: $J_L=J_0(e^{V_{OC}/V_T}-1)$. Increasing light intensity by a factor of 20 multiplies $J_L$ by 20.
Since $V_{OC}/V_T=18.04$, the exponential is much larger than one. Taking the ratio gives the accurate approximation $\Delta V_{OC}=V_T\ln20$.
Thus $V_{OC,new}=0.451+0.025\ln20=$ **0.52589 V**, within the official 0.51–0.62 V interval. The voltage rises logarithmically, not by a factor of twenty.