Let's work through the **step-by-step solution** for the non-inverting op-amp circuit shown. --- ### **a. Verify the DC gain is correct** For a **non-inverting amplifier**: \[ V_{out} = V_{in} \left( 1 + \frac{R_3}{R_4} \right) \] Given: - \( R_3 = 10\,k\Omega \) - \( R_4 = 5.1\,k\Omega \) So, the **DC gain (A_v)** is: \[ A_v = 1 + \frac{R_3}{R_4} = 1 + \frac{10\,k}{5.1\,k} \] \[ A_v = 1 + 1.96 = 2.96 \] **Theoretical DC gain = 2.96** --- ### **b. Verify the phasing of \( V_{out} \) relative to \( V_{in} \) with an AC signal at \( V_{in} \)** In a **non-inverting amplifier**, the output signal is **in phase** with the input signal (no phase inversion). So, if you apply a sine wave to \( V_{in} \), the output \( V_{out} \) will be a sine wave of greater amplitude, but with **the same phase** as \( V_{in} \). --- ### **c. Measure the largest peak input signal before the output saturates** The **output swing** of a 741 op-amp is slightly less than the supply rails due to headroom limitations. Typically, for ±10V supplies, the output can swing to about ±8.5V (depends on the op-amp). Let’s denote the maximum output swing as \( V_{out(max)} \approx \pm 8.5V \). The maximum **peak input** before output saturation: \[ V_{out(max)} = A_v \cdot V_{in(max)} \] \[ V_{in(max)} = \frac{V_{out(max)}}{A_v} \] \[ V_{in(max)} = \frac{8.5}{2.96} \approx 2.87\,V \] So, the **maximum peak input amplitude** is approximately **2.87V**. --- ### **d. Draw the input and output waveforms (use any sinusoid at \( V_{in} \)). Does this meet your expectation?** **Waveforms:** - \( V_{in} \): Sine wave of amplitude, say, 1V. - \( V_{out} \): Sine wave of amplitude \( 2.96 \times 1V = 2.96V \), in phase with \( V_{in} \). **Sketch:** - Both signals are sine waves. - Both start at the same time (no phase shift). - Output waveform is stretched vertically compared to the input. **Expectation:** Yes, this matches the expected behavior of a non-inverting op-amp amplifier. --- ## **Summary Table** | Step | Result | |------|--------| | **a. DC Gain** | \( 2.96 \) | | **b. Phase** | Output is **in phase** with input | | **c. Max input** | \( \approx 2.87\,V \) peak | | **d. Waveforms** | Output is a magnified, in-phase sine wave | --- **If you need to see a drawn waveform, let me know!**