P 6.4-1 Determine the node voltages for the circuit shown in Figure P 6.4-1.

Answer: v_a = 2 V, v_b = – 0.25 V, v_c = – 5 V, v_d = – 2.5 V, and v_e = – 0.25 V

Figure P 6.4-1

From the op-amp rules, we know

We cannot use node d for voltage node equation directly as the op-amp is an unknown current source or sink, the equation above is the result of the presence of the op-amp. Now we have two voltage sources so we have two equations that are

Now we can write voltage node equations for , and

and

Using the first of these two node equations we can plug in the known values of and

Multiply by 40 kΩ

From our op-amp equation we know now we can use the other node equation to find .

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This page last updated on March 14, 2019