CHAPTER 1. DIRECT CURRENT CIRCUITS12I3IR3R2R1Figure 1.5: Example current divider.V = R123I =R1R2R3R1R2 + R2R3 + R3R1I.(1.18)whereV is the common voltage across the three parallel resistors. The currentthroughR3 is thusI3 =VR3=R1R2R1R2 + R2R3 + R3R1I.(1.19)Now lets consider some general approaches to solving for unknowns in circuits.1.3.4Branch Current MethodUse both of Kirchoﬀ’s laws. But be aware that an arbitrary application of Kirchoﬀ ’s twoequations will not always yield an independent set of equations. But the following approachwill probably work.1. Label the current in each branch (do not worry about the direction of the actualcurrent).2. Use only interior loops and all but one node.3. Solve the system of algebraic equations.1.3.5Loop Current MethodThis method is also referred to as the mesh loop method. The independent current variablesare taken to be the circulating current in each of the interior loops.1. Label interior loop currents on a diagram.2. Obtain expressions for the voltage changes around each interior loop.3. Solve the system of algebraic equations.Depending on the problem, it may ultimately be necessary to algebraically sum two loopcurrents in order to obtain the needed interior branch current for the ﬁnal answer.