Theory

To Verify Millman's Theorem.  

This theorem is a combination of Thevenin's and Norton's theorems. When a number of voltage sources (`V<sub>1</sub>`,`V<sub>2</sub>`,...,`V<sub>n</sub>`) are in parallel having internal resistances (`R<sub>1</sub>`,`R<sub>2</sub>`,...,`R<sub>n</sub>`) respectively, the arrangement can be replaced by a single equivalent voltage source `V` in series with an equivalent series resistance `R` as given below in Fig.1 and Fig.2.

     

As per Millman's Theorem ,

                                                 $$V = (+- V_1G_1 +- V_2G_2 +-.........+- V_nG_n)/(G_1+G_2+.........+G_n)$$

                                                                                            where $$G_i = 1/R_i$$,    $$i = 1,2,....,n$$

                                                 $$R=1/G=1/(G_1+G_2+.........+G_n)$$

This voltage represents the thevenin's voltage `V`. The resistance `R` can be found , as usual , by replacing each voltage source by a short circuit. If there is a load resistance R_L across the terminals A and B , then the load current I_L` is given by

                                                $$I_L=V/(R+R_L)$$