What is the Function of the AC Source?

Here are the two golden rules of an ideal op-amp in the negative feedback configuration:

1) The currents into the two terminals (+ and -) are zero
2) The voltages at the two terminals (+ and -) are the same

Analysis:

a) No current into the + terminal $\implies v_+ = v_{AC}$
b) Rule (2) $\implies v_- = v_+ = v_{AC}$
c) Connection of - terminal to output means that the voltage across the $3 \Omega$ resistor is $v_{AC}$

Power across $3 \Omega$ resistor:

$P(t) = \frac{v^2_{AC}(t)}{R_{3 \Omega}}$

d) AC source in series with the + op-amp terminal $\implies$ no power supplied by AC source
e) All power sourced by the DC source

Power equivalence:

$P(t) = \frac{v^2_{AC}(t)}{R_{3 \Omega}} = v_{DC} \, i_{DC} (t) \\ i_{DC} (t) = \frac{v^2_{AC}(t)}{R_{3 \Omega} \, v_{DC}} \\ i_{DC} \, \text{max} = \frac{5^2}{3 \times 10} \approx 0.8333$

We see, therefore, that the AC source modulates the power output of the DC source, but doesn't supply any power itself. At a high level, the AC voltage can be thought of as a control signal for a physical process.