In a closed circuit, what must be true about the sum of voltages?

In a closed circuit, the sum of the voltages must equal zero for energy conservation due to Kirchhoff's Voltage Law (KVL), which states that the sum of the electrical potential differences (voltages) around any closed loop in a circuit must be equal to zero. This is grounded in the principle of conservation of energy, whereby the total energy supplied by sources (like batteries) must be used by the components in the circuit (like resistors, capacitors, etc.) without any loss in energy.

When you walk around a circuit loop, you can measure voltage rises (such as across a battery) and voltage drops (such as across resistors). According to KVL, if you tally these voltages, the total should balance out to zero; that is, the total amount of energy gained and lost in the circuit through voltage changes is equal, signifying continuity within the system.

The understanding of KVL is fundamental in circuit analysis, as it aids in the design, troubleshooting, and maintenance of various electronic systems and devices. This principle ensures that no energy is created or destroyed within the circuit, reinforcing the foundational laws of thermodynamics in electrical engineering contexts.