Question

R₁​ = R₂ = 100Ω

R₃ ​= R₄​ = 200​Ω

By hand, calculate the unknown currents, I₁ and I₂​ using the three methods below and attach after this sheet.
a) Inverse Matrix Method
b) Cramer's Rule
c) Substitution

NOTE: Use the following matrix setup (Take Vₛ​ to be 7) :

[(R₁ + R₂​) − R₂ ] [I₁] = [Vₛ]
[ ​​−R₂ (R2₂+R₃​+R₄​)​] [I₂​​​] [ ​0​]

Write a MATLAB code implementing the Inverse Matrix Method. Check your answer with Left Division. Attach after this sheet: (both cases where VSₛ=5 and 7V)
a) m-file
b) output

Answer 1

To solve the circuit and find the unknown currents, we can use Kirchhoff's laws. Start by applying Kirchhoff's junction rule at point A to obtain the equation I₁ = I₂ + I₃. Next, apply Kirchhoff's loop rule in the upper and lower loops to obtain the equations V₁ = I₁R₁ + I₂R₂ and -V₂ = I₂R₂ - I₃(R₃+R₄).

Step-by-step explanation:

To solve the circuit and find the unknown currents, we can use Kirchhoff's laws. Start by applying Kirchhoff's junction rule at point A to obtain the equation I₁ = I₂ + I₃. Next, apply Kirchhoff's loop rule in the upper and lower loops to obtain the equations V₁ = I₁R₁ + I₂R₂ and -V₂ = I₂R₂ - I₃(R₃+R₄). Using the given values for resistors and voltage sources, you can substitute the values into the equations and solve for the currents I₁, I₂, and I₃.