Determine the voltage gain of the circuit in Fig. P4.9

Assuming an ideal op-amp, determine the voltage gain of the circuit in Fig. P4.9.

Image from: J. D. Irwin and R. M. Nelms, Basic engineering circuit analysis, 10th ed. Hoboken, NJ: John Wiley, 2011.

Solution:

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As we are treating this to be an ideal op-amp, remember the following:

Looking at the diagram, we see that the positive terminal has a value of V_1 because there is a direct source feeding a voltage of V_1, therefore, the value at the negative terminal must also be V_1. Let us illustrate this as follows:

Notice how the node attached to the negative terminal (colored purple) has a value of V_1. Also note the arbitrarily chosen currents flowing in and out of the node. Remember that I_3=0 A because as mentioned, no current flows in or out of the positive and negative terminals in the op-amp. Let us now focus on the orange colored node. The voltage at that point is 0 V, since the bottom node is grounded (this is required to maintain Kirchhoff’s current law KCL) .

Let us now write KCL at the purple node:

Final Answer:

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 4, question 4.9.