The sum of all voltage changes around any closed loop in a circuit must equal zero: $\sum \Delta V = 0$.

$\Delta U_{E} = q \Delta V$, where $\Delta U_{E}$ is the change in electric potential energy, $q$ is the charge, and $\Delta V$ is the change in electric potential (voltage).

The sum of all voltage changes (potential differences) as you go around a closed loop in a circuit is zero.

An increase in electric potential, typically provided by a battery or other voltage source.

A decrease in electric potential, typically occurring across a resistor due to energy dissipation.

1. Identify closed loops in the circuit. 2. Choose a direction to traverse each loop. 3. Sum the voltage changes around each loop, using sign conventions (positive for voltage gains, negative for voltage drops). 4. Set the sum equal to zero: $\sum \Delta V = 0$. 5. Solve for unknown variables.

If the loop is traversed in the direction of current flow, the voltage change is negative (voltage drop). If traversed against the current flow, the voltage change is positive.

If the loop is traversed from the negative to the positive terminal, the voltage change is positive (voltage gain). If traversed from the positive to the negative terminal, the voltage change is negative.

Draw a clear circuit diagram and label all known and unknown values, including voltage sources, resistors, and current directions.

Solve the system of equations using algebraic methods such as substitution or matrix operations to find the unknown currents and voltages.

The sum of all voltage changes around any closed loop in a circuit must equal zero.

The energy a charge possesses due to its position in an electric field.

The difference in electric potential between two points; also known as voltage.

The decrease in electric potential across a circuit element, such as a resistor.

The increase in electric potential provided by a source, such as a battery.