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Question : Does a solar cell generate electricity when it is cloudy?

The solar radiation consists of 2 contributions:

1) the direct solar radiation
2) the diffuse radiation.

At a cloudless sky, the beams of the sun fall directly on the solar panel. We call this direct solar radiation.
But when there are a lot of clouds (by day), it is still light. In this case we speak of diffuse radiation, and also diffuse radiation generates electricity in a solar cell. Light particles (photons) enter the solar cell, and produce therefore electricity.

The atmosphere absorbs a part of the direct solar radiation, and re-emits it as diffuse radiation.
In e.g. Western-Europe, the contribution of direct and diffuse solar radiation is approximately just as important. (see also: "How can you orientate a solar panel?”)

It is therefore a fairy tale that no solar energy is produced on a cloudy rainy day (but there is less production then on a sunny day).

Answer : yes!