QB_PH_SEC8_004: Operational Amplifiers & Analog Circuits

A non-inverting operational amplifier circuit is constructed with input resistor $R_1 = 5\text{ k}\Omega$ connected to ground and feedback resistor $R_f = 45\text{ k}\Omega$. If an input voltage of $V_{\text{in}} = 1.2\text{ V}$ is applied to the non-inverting terminal, find the output voltage $V_{\text{out}}$ in Volts.

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Ideal Op-Amp Voltage Follower Feedback**: - Inverting terminal voltage: $V_- = V_{\text{out}} \frac{R_1}{R_1 + R_f}$ - By virtual short concept: $V_- = V_+ = V_{\text{in}}$ 2. **Gain Derivation**: $V_{\text{in}} = V_{\text{out}} \frac{R_1}{R_1 + R_f} \implies V_{\text{out}} = \left(1 + \frac{R_f}{R_1}\right) V_{\text{in}}$ 3. **Numerical Computation**: $V_{\text{out}} = \left(1 + \frac{45\text{ k}\Omega}{5\text{ k}\Omega}\right)(1.2\text{ V}) = (1 + 9)(1.2) = 10 \times 1.2 = 12\text{ V}$ 4. **Official Answer**: 12 V.