The question is how does the effect of a sound or music create different moods? The ragas are so composed that the notes or Swaras are arranged in a particular fashion. For ex: in a melakarta raga, all seven notes appear in order both in the ascent and descent as well. Whereas, in the janya ragas, it may so happen that one or more Swaras may be either excluded or appear in zigzag form or it might borrow an alien Swara too. Thus we have a complex combination of Swaras which in turn produces different vibrations. When vibrations differ, the corresponding mood/emotion differs too.
Emotions or moods are the interpretation of physical changes in our body, in response to an external stimuli, as per James-Lange theory of emotion. The Carnatic ragas are such external stimuli and hence interpreted as responsible for mood changes in an individual. A combination of Swaras in a particular fashion induces an emotion in an individual. It may be a peaceful, joyous, sad/intense, blissful or many such experiences, depending on how the combo of Swaras go.
According to Bharata’s natya shastra, there are nine predominant moods or emotions, namely:

• Sringaara: Related to love, eros
• Hasya: Humorous/comic
• Bheebhatsa: disgust
• Raudra: Fury or anger
• KaruNa: Compassion or sympathy
• Veera: Heroic
• Bhayaanaka: Terrible/horrifying
• Adbhuta: Wonderment/ amazing

The emotions that emanate from these basic moods are numerous. The following chart depicts a few of them.

The ragas with their distinct combo of Swaras can stimulate one or more of the above mentioned moods.
Ex: raga Kamavardhini, as the name suggests is basically a sensuous raga, kama meaning love, vardhini meaning increase or upliftment. The effect of a raga does not cease to a single emotion as in the case of kamavardhini too. It is also sung to evoke devotion. The tempo, phrases used, pitch, lyrics and the instrument through which the raga is played are a few parameters that contribute significantly, to the effect, the raga produces. A few more examples that I would like to quote are:

• Kharaharapriya: 22^nd melakarta raga. This raga evokes bhakti rasa as well as karuna rasa.
• Hamsadhvani and mohana, janya in 29^th melakarta, evokes Veera rasa and creates a happy mood.
• Vakra (zig zag) or varjya (omited notes) ragas like kamaach, kambhoji, hindola, vasanta etc., are called rakti raagas for the raga shines basically due to their popular intricate phrases and has a potential to evoke mixed positive emotions.
• Certain ragas like saavEri, in which the jeeva swara(‘G3’) triggers a deep emotion of connecting with the higher universal plane and possess the potential to take one to ‘Samadhi’ stithi (transcendental state)

Having mentioned all the above, I would like to conclude with a note that the capability of enjoying a raga is highly subjective. Or in other words, it plays a placebo effect on the performer as well as the listeners.
 
References

• Image reference: Google images
• chakras.net
• James- Lange theory of emotion, Wikipedia