CHAPTER 1. DIRECT CURRENT CIRCUITS9(a)(b)(c)Figure 1.2: Some grounding circuit diagram symbols: a) earth ground, b) chassis groundand c) common.1.3Kirchoﬀ ’s LawsThe conservation of energy and conservation of charge when applied to electrical circuits areknown as Kirchoﬀ’s laws.Conservation of energy – zero algebraic sum of the voltage drops Vi around a closedcircuit loop (imaginary loop)iVi =0.(1.5)Conservation of charge – zero algebraic sum of the currents Ik ﬂowing into a point (totalcharge in, equals total charge out)kIk =0.(1.6)When applying these laws to solve for circuit unknowns we will ﬁnd the following deﬁni-tions useful:• an element is an impedance (resistance) or EMF (ideal voltage source or ideal currentsource),• a node is a point where three or more current-carrying elements are connected,• a branch is one element or several in series connecting two adjacent nodes, and• an interior loop is a circuit loop not subdivided by a branch.Using these deﬁnitions we can apply Kirchoﬀ’s laws to a circuit to solve for the unknownquantities. The general procedure is:1. deﬁne the currents and voltages on a diagram,2. apply Kirchoﬀ’s laws to loops and nodes,3. write down a set of linear algebraic equations, and4. solve for the unknowns.But before we look at general circuits lets consider how simple resistors add.