Question E7G09:
What will be the output voltage of the circuit shown in Figure E7-3 if R1 is 1,000 ohms, RF is 10,000 ohms, and 0.23 volts DC is applied to the input?  

Choices:  
A: 0.23 volts  
B: 2.3 volts  
C: -0.23 volts  
D: -2.3 volts    

Correct Answer is  D: -2.3 volts  

For Figure E7-3 (the standard inverting op-amp):

1) Why D (-2.3 volts) is correct
- This is an inverting amplifier. The gain is set by the ratio of the feedback resistor to the input resistor.
- Use the inverting amplifier formula:
  $$V_{out} = -\frac{R_F}{R_1} V_{in}$$
- With $R_1 = 1\,\text{k}\Omega$, $R_F = 10\,\text{k}\Omega$, and $V_{in} = 0.23\,\text{V}$:
  $$V_{out} = -\frac{10{,}000}{1{,}000} \times 0.23 = -10 \times 0.23 = -2.3\,\text{V}$$
- The negative sign indicates inversion (180-degree phase shift).

2) Why the other choices are incorrect
- A: 0.23 volts — This would be a unity-gain buffer (non-inverting follower), not the inverting amplifier shown.
- B: 2.3 volts — Correct magnitude but wrong sign; would correspond to a non-inverting gain of +10 or forgetting the inversion.
- C: -0.23 volts — Correct sign but wrong magnitude; this would occur if $R_F = R_1$ (inverting unity gain), which is not the case.

3) Useful formulas and rules of thumb
- Inverting amplifier:
  $$V_{out} = -\frac{R_F}{R_{in}} V_{in}$$
- Non-inverting amplifier:
  $$V_{out} = \left(1 + \frac{R_F}{R_{in}}\right) V_{in}$$
- Ideal op-amp “golden rules” (with negative feedback):
  - Input currents are ~0 A.
  - $V_{-} \approx V_{+}$ (virtual short). If $V_{+}$ is at ground, $V_{-}$ is a virtual ground.