Final answer:
Kirchhoff's Laws are the well-known mathematical tools used to engineer a voltmeter with the best performance, considering operational and cost restrictions. They provide a set of rules that allow us to analyze and design electrical circuits, generating equations to find unknown values in the circuit.
Step-by-step explanation:
The well-known mathematical tool used to engineer a voltmeter with the best performance, considering operational and cost restrictions, is Kirchhoff's Laws. Kirchhoff's Laws are a set of rules that apply to any circuit, allowing us to generate equations that help us find the unknown values in circuits, such as currents, voltages, and resistances.
Using Kirchhoff's Laws requires several steps, including applying the rules and making decisions about the signs of various quantities in the equations obtained. These steps help in the accurate analysis and design of electrical circuits, ultimately leading to the development of voltmeters with optimal performance.