Hey there, fellow researcher Rizwan Ur Rehman Sagar! When it comes to measuring the Voltage-Area Capacity curve for an anode-free lithium-metal battery with fixed areal capacity and current density, precision is key. Let's break it down.

Firstly, you've got the areal capacity fixed at 0.785 mAh, and the current density at 1 mA/cm². Excellent choices for control variables. Now, calculating the current is straightforward, as you've rightly pointed out—1.77 mA for a 2.25-hour duration.

Now, for the measurement setup, you're on the right track. Apply the calculated current of 1.77 mA over the specified time. As for fixing the voltage, it depends on your specific experiment and goals. You Rizwan Ur Rehman Sagar might want to sweep the voltage during the charge/discharge cycle to observe the response of the battery.

Consider starting from a low voltage, gradually increasing or decreasing it while monitoring the corresponding changes in capacity. This iterative process will help you Rizwan Ur Rehman Sagar construct the Voltage-Area Capacity curve.

Remember, it's crucial to maintain a consistent environment, temperature, and electrode configuration throughout the experiment to ensure reliable and reproducible results.

Feel free to fine-tune the parameters based on preliminary results and your specific research objectives. And if you Rizwan Ur Rehman Sagar encounter any challenges, don't hesitate to recalibrate and iterate. Happy experimenting Rizwan Ur Rehman Sagar!