Question

c. Solve the equations for l s, la, and ls. Once you have your equations, show them to your instructor for approval before continuing to the rest of the lab. Build the circuit and set V1 = 5.00 V and V,-100V-Be careful to make sure your leads in and out of the power supplies are correct! Do not turn on the power supplies yet 2. Using the values for resistance and voltage given and the equations you derived for the currents, complete the following table: 3. Calculations Table 1 Theoretical current from Kirchhoff's Rules (mA) Resistor Values (2) R 150 R2 220 R3 470 - 18.6 la 12.6

those are my equations, need help on part C

Answer 1

I₁ = I₂ + I₃ ........................1

R₁I₁ + R₂I₂ = V₁ - V₂ .........2

R₃I₃ - R₂I₂ = V₂ .................3

from equation 1 and 2, we get,

R₁I₂ + R₁I_{3 +} R₂I₂ = V₁ - V₂ ...4

multiplying eq 3 with R₁ and equation 4 with R₃ and substractiong, we get,

R₁R₃I₂ + R₁R₃I_{3 +} R₂R₃I₂ - (R₁R₃I₃ - R₁R₂I₂) = V₁R₃ - V₂R₃ - V₂R₁

or, (R₁R₃+R₂R₃+ R₁R₂)I₂ = V₁R₃ - V₂(R₃ + R₁)

or, I₂ = {V₁R₃ - V₂(R₃ + R₁)}/(R₁R₃+R₂R₃+ R₁R₂) .......................a

from eq 3,

I₃ = {V₂ + R₂I₂ }/R₃ = (V₂R₁ + V₁R₂)/(R₁R₃+R₂R₃+ R₁R₂) .............b

from eq 1

I₁ = I₂ + I₃ = (V₁R₂ + V₁R₃ - V₂R₃)/(R₁R₃+R₂R₃+ R₁R₂) ...........c