Understanding the Question: We are asked for the output voltage of an inverting amplifier when the input and feedback resistors are the same.
Key Formulas and approach: The output voltage $V_o$ for an inverting amplifier is:
\[ V_o = -\left( \frac{R_f}{R_{in}} \right) V_{in} \]
Detailed Solution:
Step 1: Given values. We are told that the feedback resistance ($R_f$) equals the input resistance ($R_{in}$). So, $R_f = R_{in}$.
Step 2: Calculating the Gain.
\[ \text{Gain} = -\frac{R_f}{R_{in}} = -\frac{R_{in}}{R_{in}} = -1 \]
Step 3: Final Result. Since the gain is $-1$, the output voltage $V_o$ is $(-1) \times V_{in}$.
Conclusion: $V_o = -V_{in}$.