• The charge that flows into a junction must be equal to the charge that flows out of that junction. Equavelently, the total current flowing into a junction is equal to the total current leaving the junction. For a simple branch this would look like:
  

• This rule is a consequence of the fact that the flow of charge is conserved in steady-state flow. There would be a build up of charge at any circuit junction if less charge flowed out of the junction than flowed into the junction. This could happen but it is assumed (unless otherwise stated) that we will be looking at the steady-state flow conditions in a circuit.

• For any closed loop you can trace in a circuit, the total potential energy (voltage) gained through emf sources must equal the total voltage drops due to the presence of resistors, capacitors, or inductors in the closed loop.
• For a circuit with only resistance, this would look like:

• This rule is a consequence of fact that work is path independent. The work required to move a charge around a closed path in a electric field is always zero. In a circuit the electric field is inside the wires where the charges are moving.
• The voltage across a resistor could be either a drop or a gain depending upon the direction of the current and the direction of the loop you choose. If the direction of the loop is opposite to the flow of current then thr voltage across a resistor is a gain and not a drop as it is when the loop direction and the current direction is the same. See voltage gain and drops in a circuit element.

Applying Kirchhoff's Rules