Question

Consider the following circuit of resistors: VA o Volts All the resistors have the same resistance R. The power rail at the top is at voltage V+ What are the other four voltages, Vi to V4? 5V. To answer this question we use Ohm's law and the Kirchhoff current law, which says that the total net current flow out of (or into) any junction in a circuit must be zero. Thus for the unction at voltage Vi, for instance, we have or equivalently a) Write similar equations for the other three junctions with unknown voltages. b) Write a program to solve the four resulting equations using Gaussian elimination and hence find the four voltages (or you can modify a program you already have, such as the program gausselim py in Example 6.1)

this program need on Spyder of python

Answer 1

a)for V_1,

4V₁-V₂-V₃-V₄=V+

for V_2,

V₂-V₁/R+V₂-0/R+V₂-V₄/R=0

=>V₂-V₁+V₂-0+V₂-V₄=0xR

=>2V₂-V₁-V₄=0

for V_3,

V₃-V₊/R+V₃-V1/R+V₃-V₄/R=0

3V_3-V₁-V₄=V₊

for V_4,

V₄-V₁/R+V₄-V2/R+V₄-V3/R+V₄-0/R=0

4V₄-V₁-V₂-V₃=0

These are the similar equations