Problem 6.4-7

For the ideal op amp on the left, we will use V₁₁ as the inverting input node voltage and V₁₂ as the noninverting input node voltage. For the one on the right, we will use V₂₁ as the inverting input node voltage and V₂₂ as the noninverting input node voltage.

We have i₀ = i1 – i2, where i1 is the current from the left hand side of the circuit and i2 is the current going to the right side of the circuit.

Let us not forget that the currents going inside the op amp are all equal zero.

By definition we have V₁₁ = V₁₂ and V₂₁= V₂₂ but V₁₂ = V₂₂ = 0 V

We have V₁₁ = Vs – R1*i1 = 0

Thus i1 = Vs/R1

We have V₀ = – R4*i2

Let V be the voltage at the node between R2 and R3.

We have V = R3*i2 on the right and V = – R2*i1 = – R2*Vs/R1 on the left side

Thus we get R3*i2 = – R2*Vs/R1 so