Problem + Hard 47-1    Font:    Problem 5.38 - page 120 -    NILSSON - RIEDEL -    Book: Electric Circuits - 8th edition - Ed. Pearson Education do Brasil - 2010.

Determine V₁ and V₂ in the circuit shown in the Figure 47-01.1 knowing that operational amplifiers are ideal.

Solution of the Problem + Hard 47-1

Knowing that, virtually, the negative input voltage must be equal to the input voltage positive of the operational amplifier, so we know that V_a = 10 V and V_b = 5 V . Using this information we can calculate the value of i₄, or:

Using this information we can also calculate the value of i₅, or:

And now we easily calculate the value of i₃, because we know that:

With the values ​​of i₃ and V_b we can calculate the value of V₂, or:

Note that as we know the values ​​of V_a and V₃ is possible to calculate the value of i₂, because:

Now, as we already know the values ​​of i₅ and i₂ we can easily calculate the value of i₁, because:

At this point we are able to calculate the value of V₁, or: