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Navy Electricity and Electronics Training Series (NEETS)
Module 1—Introduction to Matter, Energy, and Direct Current
Chapter 3:  Pages 3-71 through 3-80

Module 1—Introduction to Matter, Energy, and Direct Current
Pages i - ix, 1-1 to 1-10, 1-11 to 1-20, 1-21 to 1-30, 1-41 to 1-50,
1-51 to 1-60, 1-61 to 1-65, 2-1 to 2-10, 2-11 to 2-20, 2-21 to 2-29,
3-1 to 3-10, 3-11 to 3-20, 3-21 to 3-30, 3-31 to 3-40, 3-41 to 3-50,
3-51 to 3-60, 3-61 to 3-70, 3-71 to 3-80, 3-81 to 3-90, 3-91 to 3-100,
3-101 to 110, 3-111 to 3-120, 3-121 to 3-126,
Appendix I, II, III, IV, V, Index

 
 
Solution:

formulas - RF Cafe



Since R3  = R4  = R5   and the voltage across each branch is the same:

formulas - RF Cafe



Solving for total resistance. Given:

formulas - RF Cafe


 

3-71




Solution:

formulas - RF Cafe



An alternate method for solving for RT  can be used.  By observation, you can see that R3, R 4, and R5 are equal ohmic value. Therefore an equivalent resistor can be substituted for these three resistors in solving for total resistance.

Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



The circuit can now be redrawn using a resistor labeled Reqi  in place   R3, R4, and R5  as shown in figure 3-51.
 

3-72



First equivalent parallel circuit - RF Cafe


Figure 3-51.—First equivalent parallel circuit.



An equivalent resistor can be calculated and substituted for R1 and R2  by use the product over the sum formula.

Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



The circuit is now redrawn again using a resistor labeled Req2  in place R1  and R2  as shown in figure 3-52.
 

3-73



Second equivalent parallel circuit - RF Cafe

Figure 3-52.—Second equivalent parallel circuit.



You are now left with two resistors in parallel. The product over the sum method can now be used to solve for total resistance.

Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



This agrees with the solution found by using the general formula for solving for resistors in parallel. The circuit can now be redrawn as shown in figure 3-53 and total current can be calculated.
 
 

3-74



Parallel circuit redrawn to final equivalent circuit - RF Cafe

Figure 3-53.—Parallel circuit redrawn to final equivalent circuit.



Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



This solution can be checked by using the values already calculated for the branch currents. Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe


 
 

3-75




Now that total current is known, the next logical step is to find total power. Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



Solving for the power in each branch. Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



Since 1R3 = 1R4 = 1R5  then, PR3 = PR4 = PR5 = 1800 W. The previous calculation for total power can now be checked.
 
 

3-76




Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



Q39.  What term identifies a single resistor that represents total resistance a complex circuit?

Q40.  The total power in both series and parallel circuits is computed with the formula: PT = P1 + P2  + P3  + ...Pn. Why can this formula be used for both series and parallel circuits?
 
Q41.  A circuit consists three resistors connected in parallel across a voltage source. R1 = 40  , R2 = 30 Ω , R3 = 40 Ω , and PR3 = 360 watts. Solve for RT, ES and 1R2. (Hint: Draw and label the circuit first.)


SERIES-PARALLEL DC CIRCUITS



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

3-77



Example combination circuit - RF Cafe

Figure 3-54.—Example combination circuit.



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

Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



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).
 
 

3-78




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

formulas - RF Cafe



Solution:

formulas - RF Cafe



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

To find total current in the circuit: Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



To find total power in the circuit:
Given:

formulas - RF Cafe


 
 

3-79




Solution:

formulas - RF Cafe



To find the voltage dropped across R1, R2 , and R3 , refer to figure 3-54(B). Req1  represents the parallel network R2 and R3. Since the voltage across each branch a parallel circuit is equal, the voltage across Req1  (Eeq1) will be equal to the voltage across R2 (ER2) and also equal to the voltage across R3 (ER3).

Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



To find power used by R1: Given:

formulas - RF Cafe



Solution:

formulas - RF Cafe



 

3-80



Introduction to Matter, Energy, and Direct Current, Introduction to Alternating Current and Transformers, Introduction to Circuit Protection, Control, and Measurement, Introduction to Electrical Conductors, Wiring Techniques, and Schematic Reading, Introduction to Generators and Motors, Introduction to Electronic Emission, Tubes, and Power Supplies, Introduction to Solid-State Devices and Power Supplies, Introduction to Amplifiers, Introduction to Wave-Generation and Wave-Shaping Circuits, Introduction to Wave Propagation, Transmission Lines, and Antennas, Microwave Principles, Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction to Microelectronics, Principles of Synchros, Servos, and Gyros, Introduction to Test Equipment, Radio-Frequency Communications Principles, Radar Principles, The Technician's Handbook, Master Glossary, Test Methods and Practices, Introduction to Digital Computers, Magnetic Recording, Introduction to Fiber Optics

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