Generalised Form of Millman’s Theorem
Generalised Form of Millman’s Theorem :
The Millman’s theorem is particularly useful for solving many circuits which are frequently encountered in both electronics and power applications.
Consider a number of admittances G1, G2, G3… Gn which terminate at common point 0′ as shown in the figure given below. The other ends of the admittances are numbered as 1, 2, 3….n. Let O be any other point in the network. It should be clearly understood that it is not necessary to know anything about the inter-connection between point O and the end points 1, 2, 3…n. However, what is essential to know is the voltage drops from 0 to 1, 0 to 2, … 0 to n etc.
According to this theorem, the voltage drop from 0 to 0′ (Voo) is given by
Proof
Voltage drop across G1 = V10′ = (V00′ − V01)
Current through G1 = I10′ = V10′ G1 = (V00′ − V01) G1
Similarly, I20′ = (V00′ − V02) G2
I30′ = (V00′ − V03) G3
……………………………..
……………………………..
and In0′ = (V00′ − V0n) Gn
By applying KCL to point 0′ , we get
I10′ + I20′ + …… + In0′ = 0
Substituting the values of these currents, we get
Precaution :
It is worth repeating that only those resistances or admittances are taken into consideration which terminate at the common point. All those admittances are ignored which do not terminate at the common point
Read article – Units of Resistivity
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