QB_PH_SEC8_001: Operational Amplifiers & Analog Circuits

In an ideal inverting operational amplifier circuit, the input resistor is $R_1 = 10\text{ k}\Omega$ and the feedback resistor is $R_f = 100\text{ k}\Omega$. If the input voltage is $V_{\text{in}} = 0.5\text{ V}$, what is the magnitude of the output voltage $|V_{\text{out}}|$ in Volts?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Ideal Op-Amp Virtual Ground**: Due to infinite open-loop gain and zero input bias current, the non-inverting terminal is grounded ($V_+ = 0$), maintaining $V_- = 0$ via negative feedback. 2. **KCL at Inverting Node**: $\frac{V_{\text{in}} - 0}{R_1} + \frac{V_{\text{out}} - 0}{R_f} = 0 \implies V_{\text{out}} = -\frac{R_f}{R_1} V_{\text{in}}$ 3. **Numerical Computation**: $V_{\text{out}} = -\left(\frac{100\text{ k}\Omega}{10\text{ k}\Omega}\right)(0.5\text{ V}) = -10 \times 0.5\text{ V} = -5.0\text{ V}$ 4. **Magnitude Request**: $|V_{\text{out}}| = 5.0\text{ V}$. Correct answer is 5.