Problem 46-1    Source:  Problem elaborated by the author of the site.

For the circuit shown in the Figure 46-01.1, calculate V_o and the current I.

Solution of the Problem 46-1

Notice that Opamp1 is in the inverter configuration. Therefore, easily we can calculate the gain of the circuit to the closed loop using the equation below.

From the circuit R_i = 2 kΩ and R_f = 8 kΩ. Substituting these values into the above equation, we have:

Calculating the value of V₂, or:

In possession of the value of V₂ the value of I can be calculated. Like this:

To calculate the value of V_o, we write the equations for the a node of Opamp 2. Then:

For an operational amplifier ideal , is valid the relation already studied where V_a = V_b = 0.5 V. Rearranging the equation for V_o we obtain the following relation:

Performing the numerical substitution and calculating V_o, we obtain:

Notice the fact that, Opamp2 operates in an inverting configuration for the output voltage V₂, while for the source of 0.5 volts, it operates in a configuration non-inverting. For this reason the output voltage V₂ é amplificado por um fator 2, while the 0.5 volt source is amplified by a factor 3.