Problem 45-3    Source:    Problem 5.39 - page 120 -    NILSSON & RIEDEL -    Book: Circuitos Elétricos - 8ª edição - Ed. Pearson Education do Brasil - 2010.

In the circuit show in Figure 45-03.1, the resistor R_x is set so that the ideal operational amplifier is exactly at the point of saturation. Determine the value of R_x in kΩ.

Solution of the Problem 45-3

Initially, one must investigate whether the voltage at the output will be positive or negative. With this, it must be determined whether the output voltage at saturation will be 20 volts (if it is positive) or equal to - 10 volts (negative case). We know (by the circuit) that the voltage at the input is negative and equal to - 4 volts. When amplified by the inverter input of the operational amplifier, a positive voltage is generated in the output. Therefore, it is concluded that V_o = 20 volts. Using a voltage divider to calculate the value of V_b and remembering that V_i = -4 volts, we obtain:

It is also known that, virtually, V_a = V_b = -0.8 volt. As we know the value of the input voltage, then we can calculate the current that flows through of the resistance of 2 kΩ. Then:

Now, this current is the same that flows through of the R_x.Thus we can calculate the value of this resistance because: