The algebraic sum of voltages around any closed path in a network is equal to ____________.

The algebraic sum of voltages around any closed path in an electrical network is equal to zero. This is known as Kirchhoff's Voltage Law (KVL), which states that the sum of the electrical potential differences (voltages) for any closed circuit is equal to the sum of the rises in voltage minus the sum of the drops in voltage. This principle is based on the conservation of energy, as it implies that the energy supplied by the sources is equal to the energy consumed by the components within the circuit.

In essence, when you traverse a loop in a circuit, accounting for the directions of voltage rises and drops, you will always end up with a net result of zero. This fundamental law is crucial for analyzing electrical circuits and ensures that all voltages and currents in a system ultimately balance out.