When a charged particle is moved from a point to another, the work
done is 
, where V is the voltage across the two points
and 
is the amount of charge on the particle. Consider a
particular case where the two points are actually the same point in
the circuit. In this case, the work done is zero. By the same
argument, if a unit charge is moved around a closed path such as the
square path shown in figure 1.7, the work done is zero, i.e.,
Figure 1.7: Kirchhoff's voltage law
Formally, KVL states that the algebraic sum of the voltages
between successive nodes in a closed path in a circuit is equal to
zero. In mathematical form, for a closed path with successive nodes
, KVL states that
where 
is the voltage between nodes j and k.
Remarks -- Any circuit that has a solution must satisfy Kirchhoff's laws. From the properties of independent sources, we can immediately conclude that a circuit cannot be solved if there exists a loop that is formed exclusively of independent voltage sources. Thus, short-circuiting an independent voltage source, as remarked earlier, is a particular case where KVL is violated. Similarly, a circuit cannot be solved if there exists a node to which only independent current sources are connected. Also, open-circuiting an independent current source is a particular case where KCL is violated.