The Shulhan Aruch (Orah Haim 275), based on the Gemara, writes that it is forbidden to read by candlelight on Shabbat. The Sages were concerned that the light might flicker, and one may then tilt the lamp so that the oil will be drawn more steadily to the wick to create a more stable flame. This would constitute a Torah violation of Shabbat, and the Sages therefore enacted a prohibition against reading by candlelight on Shabbat.
Does this prohibition apply as well to electric lights? Would it be forbidden to read by the light of an electric bulb on Shabbat, since here, too, the bulb might go out and one may then replace it, in violation of Shabbat?
Hacham Bension Abba Shaul addresses this question in his work Or Le’sion (vol. 18, Siman 18), and writes that generally speaking, the Rabbinic enactment would not apply to reading by the light of an electric bulb. He notes that the Sages forbade reading by candlelight not out of the concern that the oil might be depleted and one will then add oil to the lamp, but rather because one might tilt the lamp. The Sages did not suspect that somebody would forgetfully add oil to a lamp on Shabbat; they were concerned only that one might tilt the lamp to bring the oil closer to the wick. In the case of an electric bulb, there is no parallel concern. The light produced by the bulb is steady and cannot be enhanced by tilting or any other action. The concern that the bulb might burn out, and that the person will then replace it, resembles the concern that the oil will run out and one will then add more oil. Since the Sages did not harbor such a concern in the case of oil lamps, it is permissible to read by the light of an electric bulb on Shabbat.
However, Hacham Bension adds, this line of reasoning would not apply to electric lights equipped with dimmers, which can be adjusted to increase or decrease the light produced by the bulb. These lights, it would appear, indeed resemble oil lamps, in that there is a possibility of adjusting the amount of light produced. Therefore, Hacham Bension rules, it would be forbidden to read by a light with a dimmer on Shabbat, just as it is forbidden to read by candlelight. Hacham Bension makes an exception in cases where Bittul Torah (missing time of Torah learning) is at stake, such as if one does not have access to any other lights and wishes to learn Torah. It is possible to distinguish between the cases of a dimmer and an oil lamp, in that the light produced by an electric light is always steady. Unlike the flame of an oil lamp, which occasionally flickers and might lead a person to tilt the lamp, an electric light – even one with a dimmer – is constant. One might argue, then, that the Sages would not be concerned that a person would adjust the dimmer while reading. Hacham Bension writes that one may rely on this rationale if he wishes to study Torah and the only available light is a light with a dimmer. Generally, however, one should not read on Shabbat by an electric light that has a dimmer.
Hacham Ovadia Yosef, in his Yabia Omer (vol. 9, p. 254), rules more leniently, permitting the use of a dimmer light under all circumstances. He notes that when one adjusts a dimmer to make the light brighter, he increases the flow of electricity into the bulb. This action resembles adding oil to a lamp, and not tilting the lamp. Therefore, since the Sages were not concerned that one may add more oil to the lamp, there is similarly no concern that one may adjust the dimmer to increase the electric current. More generally, Hacham Ovadia argues, after the time of the Talmud we do not have the authority to introduce new Gezerot (enactments). Electric lights did not exist in the time of Hazal, and they therefore did not forbid reading by electric lights on Shabbat. Even with the advent of electric lights, it is not within the authority of the Rabbis to introduce a new provision forbidding reading by these lights. Therefore, Hacham Ovadia contends, one may read by the light of any kind of electric bulb, even if it has a dimmer, and even if there is no concern of Bittul Torah.
Summary: Even though the Sages forbade reading on Shabbat by candlelight, it is permissible to read by electric lights, even by lights with dimmers.