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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 12

Fundamentals of Electricity & Electronics

Formula: R ; 2 ; R23 = ; R ; 2

3 R 3

R2 and R3 can be reduced to R23. Figure 12-101 now shows an equivalent circuit with three series connected resistors. The total resistance of the circuit can now be simply determined by adding up the values of resistors R1, R23, and R4.

Determining the Total Resistance

A more quantitative example for determining total resistance and the current in each branch in a combination circuit is shown in the following example. [Figure 12-102]

The first step is to determine the current at junction A, leading into the parallel branch. To determine the IT, the total resistance RT of the entire circuit must be known. The total resistance of the circuit is given as:

Figure 12-97. Kirchhoff’s Current Law.
Figure 12-97. Kirchhoff’s Current Law.
Figure 12-98. Individual branch currents.
Figure 12-98. Individual branch currents.
Figure 12-99. Determining an unknown circuit in branch 2.
Figure 12-99. Determining an unknown circuit in branch 2.
Formula: RT = R1 + R23 ; Where R23 = ( ; R ; 2 R ; R ; 2

) Parallel network

Formula: 2 ; k ; Ω ; 3 ; k ; Ω ; Find REQ R23 = ; 2 ; k ; Ω ; + ; 3 ; k ; Ω ; R23 =6, ; 0 ; 0 0 ; k Ω ; 5 ; k ; Ω ; Solve for REQ ; R23 = 1.2k Ω ; Solve for RT RT = 1k Ω + 1.2k Ω ; RT = 2.2k Ω

With the total resistance RT now determined, the total IT can be determined. Using Ohm’s Law:

Formula: E ; S ; IT = ; R ; T ; 2 ; 4 ; V ; Substitute values IT = ; 2 ; .2 ; k ; Ω ; IT = 10.9 mA

The current through the parallel branches of R2 and R3 can be determined using the current divider rule discussed earlier in this handbook.

Recall Parallel Branch Resistance:

Formula: 6 ; , ; R23 = ; 5 ; ,
Formula: 0 ; 0 ; Ω ; 0 ; 0 ; Ω ; R23 = 1.2k Ω

Substitute values for I2:

Figure 12-100. Series-parallel circuits.
Figure 12-100. Series-parallel circuits.