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?           (**************************************************)
?           (*                                                *)
?           (*             Elementary Electricity             *)
?           (*                                                *)
?           (*   Tutorial No. 4                               *)
?           (*                                                *)
?           (*            Series-Parallel Resistors           *)
?           (*                                                *)
?           (*                   Version 1.0                  *)
?           (*                                                *)
?           (*   This program  illustrates how resistances    *)
?           (*   may be  connected  to include both series    *)
?           (*   and parallel branches in the same circuit.   *)
?           (*   The student is expected to calculate  the    *)
?           (*   equivalent resistance of a number of such    *)
?           (*   circuits.                                    *)
?           (*                                                *)
?           (*   Written by T. J. Meyers      July 18,l985    *)
?           (*                                                *)
?           (**************************************************)
INTRODUCTION
;    The circuits in  this program include  both series  and
;parallel branches. To arrive at correct numerical solutions
;to the problems that  follow you must first  have  mastered
<problems of the type set forth in the  preceding  tutorials.
;You can return to the menu and make a new program selection
#by typing MENU when the A> appears.
SCHEMATIC DIAGRAM I
A Series-Parallel Circuit
=                              R-1                            
=                         a           b                       
=                 ........./\  /\  /\...............          
=                 :          \/  \/                :          
=           -     :                    R-2         :          
=                _:_                               :          
=       1.5 V   _____          ..../\  /\  /\....  :          
=                 |            :     \/  \/     :  :          
=           +     :    /       :                :  :          
=                 :.../  ......:                :..:          
=                             d:       R-3      :c            
=                    sw-1      :                :             
=                              :.../\  /\  /\...:             
=                                    \/  \/                   
=                                                             
=Study this diagram carefully.  Make a good working copy on   
=a piece of paper.  You will need it.                         
SCHEMATIC DIAGRAM II
A Series-Parallel Circuit
=                     R-1                                     
=                a            b        c                      
=           ......./\  /\  /\......................           
=       -   :        \/  \/            :          :           
=          _:_                         /          /           
=  1.5 V  _____                        \ R-2      \ R-3       
=           :                          /          /           
=       +   :                          \          \           
=           :     /                     :          :          
=           :..../  ....................:..........:          
=               sw-1                    d                     
=                                                             
=Study this diagram carefully.  Make a good working copy on   
=a piece of paper. You will need it.                          
ANALYSIS OF DIAGRAMS
=Carefully compare, point by point, the two diagrams which you
=have just drawn.  Though they may appear to be different they
really are the same circuit.
=The charges leave the negative terminal of the dry cell, flow
?to point a, pass through resistor R-1 to point b, then continue
=to point c.  At point c, the charges are faced with a choice.
=They may flow either through resistor R-2 or through resistor
>R-3.  Just as a large group of people in a room with two exits
=would do, they use both paths.  Part of the charge will flow 
<through  R-2, part through R-3.  The charges then rejoin at 
>point d, flow through switch sw-1 (when closed), and return to
=the positive terminal of the cell.  How the charges apportion
=themselves between R-2 and R-3 will be left for discussion in
another tutorial.
QUESTIONS: 
5    1.  What is the total resistance of this circuit?
    2.  How do we calculate it?
3CALCULATING RESISTANCE IN A SERIES-PARALLEL CIRCUIT
@   Assume the figure below to consist of a single resistor      
@   connected in series with two resistors which are themselves  
   connected in parallel.
@                                R-2                             
@                   R-1      :-[******]-:                        
@         --------[******]---:          :--------->              
@                            :-[******]-:                        
@                                R-3                             
@   In determining the total resistance in a circuit such as this
@   the RULE is:  solve the PARALLEL branch FIRST, then add the  
@   result to the resistance (R-1) which is in series.           
PROBLEM:
9   Let R-1 = 10 ohms, R-2 = 10 ohms, and R-3 = 10 ohms.  
9   Calculate the total resistance. That is, calculate the
9   single resistance which would be equivalent to these 3
   resistances combined.
	SOLUTION:
!   1.  Solve the parallel branch:
'       R(p) = (R-2 * R-3) / (R-2 + R-3)
#            = (10 * 10) / (10 + 10)
$            =    100/20   =   5 ohms
   2.  Add the result to R-1:
,       R(total) = R-1 + (result from step 1)
,                =  10 + 5 = 15 ohms (answer)
8So to repeat our RULE:  solve the PARALLEL branch FIRST,
9then add the result to the resistance which is in series.
=The following module will give you practice in solving simple
=circuits of this type.  If you experience difficulty, you may
/wish to review the tutorial Parallel Resistors.
PROBLEMS
<You have seen one simple problem solved.  Mastery, however, 
>comes only with practice.  The following problems are provided
=to test your skill and understanding.  At a minimum, you will
need paper and pencil.
>Determine each answer using significant figures, and round off
#using standard rounding procedures.
@Remember the RULE:  first solve the parallel branch(es) then add
<                    the result(s) to the series resistor(s).
PROBLEM No. 1
Series Resistors   :  R-1 =  
25 ohms
Parallel Resistors :  R-2 =  
40 ohms
      R-3 =  
40 ohms
*The equivalent resistance in ohms is:     
&Excellent.  Now let's try problem No.2
Sorry.  Please try again.
*The equivalent resistance in ohms is:     
Good.  Now go to problem No. 2
'Wrong again.  Let's try that once more.
*The equivalent resistance in ohms is:     
#OK this time.  Now try problem No.2
Too bad.  Wrong again.
*The correct answer is                     
PROBLEM No. 2
Series Resistors   :  R-4 =  
13 ohms
Parallel Resistors :  R-5 =  
30 ohms
      R-6 =  
20 ohms
*The equivalent resistance in ohms is:     
'Excellent.  Now let's try problem No.3.
Sorry.  Please try again.
*The equivalent resistance in ohms is:     
Good.  Now go to problem No. 3.
'Wrong again.  Let's try that once more.
*The equivalent resistance in ohms is:     
%OK this time.  Now try problem No. 3.
Too bad.  Wrong again.
*The correct answer is                     
PROBLEM No. 3
Series Resistors    :  R-7 =  
Parallel Resistors  :  R-8 =  
          R-9 =  
*The equivalent resistance in ohms is:     
(Excellent.  Now let's try problem No. 4.
Sorry.  Please try again.
*The equivalent resistance in ohms is:     
Good.  Now go to problem No. 4.
'Wrong again.  Let's try that once more.
*The equivalent resistance in ohms is:     
%OK this time.  Now try problem No. 4.
Too bad.  Wrong again.
*The correct answer is                     
PROBLEM No. 4
Series Resistors    : R-10 =  
17.85
Parallel Resistors  : R-11 =  
23.65
       R-12 =  
49.75
*The equivalent resistance in ohms is:     
(Excellent.  Now let's try problem No. 5.
Sorry.  Please try again.
*The equivalent resistance in ohms is:     
Good.  Now go to problem No. 5.
'Wrong again.  Let's try that once more.
*The equivalent resistance in ohms is:     
%OK this time.  Now try problem No. 5.
Too bad.  Wrong again.
The correct answer is          
PROBLEM No. 5
Series Resistors    :  R-13 =  
Parallel Resistors  :  R-14 =  
        R-15 =  
2.2 meg
*The equivalent resistance in ohms is:     
#Excellent.  You have done them all!
Sorry.  Please try again.
*The equivalent resistance in ohms is:     
&Good.  You have completed the program.
'Wrong again.  Let's try that once more.
*The equivalent resistance in ohms is:     
OK. All done.
Too bad.  Wrong again.
The correct answer is        
CONCLUSION
Now, let us sum up:  
>1.  In an electric circuit the current flows from the negative
4    terminal to the positive terminal of the source.
@2.  When the circuit branches, as when two or more resistors are
<    connected in parallel, the current divides, part flowing
<    through each branch.  When the branches rejoin so do the
@    individual currents. The total amount of current leaving the
8    branches being exactly equal to the amount entering.
<3.  When determining the equivalent (total) resistance of a 
;    series-parallel circuit, one FIRST determines the total
>    resistance of the PARALLEL branch(es).  The result is then
$    added to the series resistor(s).
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