In theory, a photovoltaic cell (a single cell) produces a current proportional to the intensity of the incident light. This is due to the photovoltaic effect. The voltage shouldn't change, much, and so power is linearly proportional to intensity. [pdf]
No, solar panels cannot generate electricity at night because they need sunlight to produce power through the photovoltaic effect. Can moonlight charge solar panels? No, moonlight is just reflected sunlight which is way too little to generate power. [pdf]
[FAQS about Can supplementing photovoltaic panels with light at night generate electricity ]
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