Superposition in Network Analysis with Ti-84
In network analysis, the superposition theorem states that in any linear circuit with multiple independent sources, the total voltage or current response in any element is the algebraic sum of the individual responses caused by each source acting alone. It simplifies complex circuits by analyzing one source at a time.For more information about superposition just search on the internet. Op this page we will show you with an example that your calculator Ti84 plus is a helpful tool to solve network analysis problems. The electric circuit below is already analyzed with Kirchoff's second law on the page:
Using the memories of the Ti84 and the Superposition Theorem results in a fast solution for Ia.
For 60Hz voltages sources the complex schematic circuit is shown.
The current Ia is devided in 2 parts namely Ia =IaV1 + IaV2. . Each source (V1, V2) shares in the total current Ia. The current IaV1 can be calculated by short cutting Source V2 and calculaing the the part IaV1 . IaV2. can be calculated by short cutting source V1 and calculating the part IaV2. The electric circuits to calculate IaV1 and IaV2. are shown.
Now it is time to use the Ti84. First we store Z1 in mem A, Z2 in mem B en Z3 in mem C
The formula for Iav1 = V1/(Z1+(Z2*Z3)(Z2+Z3)).If we use mem D for Iav1 than D=110/(A+(B*C)/(B+C))
The formula for Iav2 = -(V2/(Z2+(Z1Z3)/(Z1+Z3)*Z3/(Z3+Z1)=-(V2*Z3)/(Z2*Z3+Z2*Z1+Z1*Z3). The minus sign because the current IaV2 is defined towards the voltage source of V2
If we use mem E for Iav2 than E=-190,52i *C/(BC+BA+AC).
Ia=Iav1+Iav2=D+E=2.35 A which corresponds with the results of Multisim and shows that the Ti84 is a helpful tool if Superposition in electric networks is applied.
