In a tala, the drtham has two units and anudrtham (if it is part of a talam) has 1 unit and this is a constant. But the units of the laghu vary according to the jaathi.  
 

Jaathi   1. Thisra Jaathi   2. Chatusra Jaathi   3. Kanta Jaathi   4. Misra Jaathi   5. Sankeerna Jaathi

Aksharams   3   4   5   7   9

So, depending upon the jaathi, the units of the laghu varies. And the jaathi of the talam is determined by the jaathi of the laghu. Also, depending upon the jaathi of the laghu, the aksharams of the tala vary. For instance, the Triputa talam has the following angams - one laghu and two drthams and symbolically 1 0 0. Now, if the Triputa is Thisra Triputa, the laghu will have three aksharams  
 

1

3

0

0

and the thala will have three aksharams. If the talam is Kanda Triputa, the laghu will have 5 aksharams and the tala will have 9 aksharams 
 

1

5

0

0

  
Thus the 7 talams in combination with the 5 jaathis gives 35 talas in Carnatic music. Among these, the Chatusra Jaathi Triputa (Adi), Rupakam, Kanda Chapu, Misra Chapu are the most widely used talam. All the 7 talas in one of the jaathi is taught in the preliminary exercise of "Alankaram". These talas are called desi talas.  
 
 

Learning Carnatic Music  Introduction Stages in Abhyasaganam -  Swaravali, Jantai Varisai, Dhatu Varisai, Melsthayi Varisai Stages in Abhyasaganam -  Alankaram, Gitam & Swarajathis, Varnams Tala Tala - Structure   Tala - Angams & Jaathis Tala - Maarga Thalams Gamakas