Series-parallel DC circuits

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Rules for Parallel DC Circuits

Matter, Energy, and Electricity

Practice Circuit Problem

SERIES-PARALLEL DC CIRCUITS

In the preceding discussions, series and parallel dc circuits have been considered separately. The technician will encounter circuits consisting of both series and parallel elements. A circuit of this type is referred to as a COMBINATION CIRCUIT. Solving for the quantities and elements in a combination circuit is simply a matter of applying the laws and rules discussed up to this point.

SOLVING COMBINATION-CIRCUIT PROBLEMS
The basic technique used for solving dc combination-circuit problems is the use of equivalent circuits. To simplify a complex circuit to a simple circuit containing only one load, equivalent circuits are substituted (on paper) for the complex circuit they represent. To demonstrate the method used to solve combination circuit problems, the network shown in figure 3-54(A) will be used to calculate various circuit quantities, such as resistance, current, voltage, and power.

Figure 3-54. - Example combination circuit.

Examination of the circuit shows that the only quantity that can be computed with the given information is the equivalent resistance of R₂ and R₃.

Given:

Solution:

Now that the equivalent resistance for R₂ and R₃ has been calculated, the circuit can be redrawn as a series circuit as shown in figure 3-54(B).

The equivalent resistance of this circuit (total resistance) can now be calculated.

Given:

Solution:

The original circuit can be redrawn with a single resistor that represents the equivalent resistance of the entire circuit as shown in figure 3-54(C).

To find total current in the circuit:

Given:

Solution:

To find total power in the circuit:

Given:

Solution:

To find the voltage dropped across R_l, R₂, and R₃, refer to figure 3-54(B). R_eq1 represents the parallel network of R₂ and R₃. Since the voltage across each branch of a parallel circuit is equal, the voltage across R_eq1 (E_eq1) will be equal to the voltage across R₂ (E_R2 ) and also equal to the voltage across R₃ (E_R3).

Given:

Solution:

To find power used by R_l:

Given:

Solution:

To find the current through R₂ and R₃, refer to the original circuit, figure 3-54(A). You know E_R2 and E_R3 from previous calculation.

Given:

Solution:

To find power used by R₂ and R₃, using values from previous calculations:

Given:

Solution:

Now that you have solved for the unknown quantities in this circuit, you can apply what you have learned to any series, parallel, or combination circuit. It is important to remember to first look at the circuit and from observation make your determination of the type of circuit, what is known, and what you are looking for. A minute spent in this manner may save you many unnecessary calculations.

Having computed all the currents and voltages of figure 3-54, a complete description of the operation of the circuit can be made. The total current of 3 amps leaves the negative terminal of the battery and flows through the 8-ohm resistor (R₁). In so doing, a voltage drop of 24 volts occurs across resistor R₁. At point A, this 3-ampere current divides into two currents. Of the total current, 1.8 amps flows through the 20-ohm resistor. The remaining current of 1.2 amps flows from point A, down through the 30-ohm resistor to point B. This current produces a voltage drop of 36 volts across the 30-ohm resistor. (Notice that the voltage drops across the 20- and 30-ohm resistors are the same.) The two branch currents of 1.8 and 1.2 amps combine at junction B and the total current of 3 amps flows back to the source. The action of the circuit has been completely described with the exception of power consumed, which could be described using the values previously computed.

It should be pointed out that the combination circuit is not difficult to solve. The key to its solution lies in knowing the order in which the steps of the solution must be accomplished.