Kirchhoff's first rule applies to *junction points* in DC circuits (*i.e.*,
points at which three or more wires come together). The junction rule is:

This rule is easy to understand. As we have already remarked, if this rule were not satisfied then charge would build up at the junction points, violating our fundamental steady-state assumption.The sum of all the currents entering any junction point is equal to the sum of all the currents leaving that junction point.

Kirchhoff's second rule applies to *loops* in DC circuits. The loop rule is:

This rule is also easy to understand. We have already seen (in Sect. 5) that zero net work is done in slowly moving a charge around some closed loop in an electrostatic field. Since the work done is equal to the product of the charge and the difference in electric potential between the beginning and end points of the loop, it follows that this difference must be zero. Thus, if we apply this result to the special case of a loop in a DC circuit, we immediately arrive at Kirchhoff's second rule. When using this rule, we first pick a closed loop in the DC circuit that we are analyzing. Next, we decide whether we are going to traverse this loop in a clockwise or an anti-clockwise direction (the choice is arbitrary). If a source of emf is traversed in the direction of increasing potential then the change in potential is . However, if the emf is traversed in the opposite direction then the change in potential is . If a resistor , carrying a current , is traversed in the direction of current flow then the change in potential is . Finally, if the resistor is traversed in the opposite direction then the change in potential is .The algebraic sum of the changes in electric potential encountered in a complete traversal of any closed circuit is equal to zero.

The currents flowing around a general DC circuit can always be found by applying
Kirchhoff's first rule to all junction points,
Kirchhoff's second rule to all loops, and then solving the
simultaneous algebraic equations thus obtained. This procedure works
no matter how complicated the circuit in question is (*e.g.*, Kirchhoff's
rules are used in the semiconductor industry to analyze the incredibly
complicated circuits, etched onto the surface of silicon wafers, which are used to
construct the central processing units of computers).