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Basic Circuit Analysis
Combination Series-Parallel Circuits
Section 3-1 Resistance in Combination Circuits
Resistive circuits in the "real world" aren't always strictly series or strictly parallel. In the "real world" of electronics, most circuits are combinations of series and parallel arrangements. Hence the general name, combination circuits. | Definition Combination Circuits Combination circuits include both series and parallel connections. | Here are examples of combination circuits:   Your objective in this chapter is to learn how to analyze combination circuits. Series-Parallel Combination Circuits | Here is one of the two major types of combination circuits. Resistor R1 is connected in series with the rest of the circuit. The rest of the circuit, consisting of resistors R2 and R3, is a parallel combination. The product-over-sum equation for total resistance of this circuit is: RT = R1 + R2 || R3 R2 and R3 are connected in parallel, and their combined resistance of is indicated by R2 || R3. Resistor R1 is connected in series with R2 and R3 , and that fact is indicated by the + sign between R1 and the other two resistors. | 
A Simple Series-Parallel Circuit
| Parallel-Series Combination Circuits | This is the second of the two major types of combination circuits. Resistor R1 is connected in parallel with the rest of the circuit. The rest of the circuit, consisting of resistors R2 and R3, is a series combination. The product-over-sum equation for total resistance of this circuit is: RT = R1 || (R2 + R3) R2 and R3 are connected in seriesl, and their combined resistance of is indicated by R2 + R3. Resistor R1 is connected in parallel with R2 and R3 , and that fact is indicated by the || sign between R1 and the other two resistors. | 
A Simple Series-Parallel Circuit
| The circuits you will be analyzing through the remainder of this chapter are extended variations of these two basic combinations. | Note  Students sometimes question the value of spending so much time solving combination circuits. The real value lies in the analytical skills that you acquire and develop by means of these exercises -- skills that apply to much more than analyzing resistor circuits, from testing circuits for the next generation of smart phones our troubleshooting a mainframe computer.
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