What is the relationship between the total voltage and the branch voltages in a parallel circuit?

In a parallel circuit, the total voltage across the entire circuit is equal to the voltage across each individual branch. This means that each branch experiences the same voltage as the total applied voltage. This property is a fundamental characteristic of parallel circuits.

When components are connected in parallel, they share the same two nodes, and thus, the voltage measured across each component (or branch) is the same as the supply voltage. Consequently, if you were to measure the voltage across any of the branches, it would match the total voltage supplied to the circuit.

This finding aligns with the principles of Ohm's Law and Kirchhoff's voltage law, which state that the sum of voltages in a closed loop must equal zero, confirming that all branch voltages cannot exceed the total voltage in a parallel configuration.

In contrast, total voltage cannot be said to equal the sum of branch voltages because this applies to series circuits, where voltages add up. Moreover, the idea that branch voltages would be higher than total voltage or could exceed it contradicts the basic laws governing electrical circuits.