Question

For an ideal op-amp, what is the output voltage if the feedback resistance is equal to the input resistance in an inverting configuration?

• A. $V_o = V_{in}$
• B. $V_o = -V_{in}$
• C. $V_o = 0$
• D. $V_o = 2V_{in}$

Hint:

Inverting amplifier gain: $A_v = -\frac{R_f}{R_{in}}$
If $R_f = R_{in}$ → Gain = $-1$

Answer 1

The Correct Option is B

Concept:
In an inverting amplifier configuration of an operational amplifier (op-amp), the input signal is applied to the inverting terminal through an input resistance $R_{in}$, while a feedback resistor $R_f$ connects the output to the inverting input. The gain of an ideal inverting amplifier is given by: \[ A_v = -\frac{R_f}{R_{in}} \]
Step 1:Applying the gain formula.
If the feedback resistance equals the input resistance: \[ R_f = R_{in} \] then the voltage gain becomes: \[ A_v = -\frac{R_{in}}{R_{in}} = -1 \]
Step 2:Determining output voltage.
Since the gain is $-1$, the output voltage is the negative of the input voltage: \[ V_o = -V_{in} \] Conclusion:
Therefore, when $R_f = R_{in}$, the output voltage of an ideal inverting op-amp is $V_o = -V_{in$}.