{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
tica-bold-r-normal--14-*" "helvetica" "Helvetica-Bold" 8 14 0 "He
lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
mes" "Times-Roman" 4 14 64 "Times-Roman" 12}{FONT 2 "-adobe-couri
er-medium-r-normal--14-*" "courier" "Courier" 4 14 192 "Courier" 
12}{FONT 3 "-adobe-new century schoolbook-bold-r-normal--17-*" "n
ew century schoolbook" "Times-Bold" 8 17 64 "Times-Bold" 17}{FONT
 4 "-adobe-new century schoolbook-bold-r-normal--14-*" "new centu
ry schoolbook" "Times-Bold" 8 14 64 "Times-Bold" 14}{FONT 5 "-ado
be-new century schoolbook-bold-r-normal--14-*" "new century schoo
lbook" "Times-Bold" 8 14 64 "Times-Bold" 14}{FONT 6 "-adobe-new c
entury schoolbook-bold-r-normal--14-*" "new century schoolbook" "
Times-Bold" 8 14 64 "Times-Bold" 14}{SCP_R 1 0 35{COM_R 2 0{TEXT 
3 18 "Wheatstone Bridge\012"}}{COM_R 3 0{TEXT 1 62 "Physics: RC c
ircuit theory\012by Tony Scott and Michael Monagan.\015"}}{COM_R 
4 0{TEXT 5 10 "Reference:"}}{COM_R 5 0{TEXT 1 112 "J.J. Brophy, `
`Basic  Electronics  for  Scientists'', 3rd edition, McGraw-Hill,
 New York,   pp. 17-19,  (1977). "}}{COM_R 6 0{TEXT 1 101 "\012Co
nsider the following circuit known as the Wheatstone bridge input
 as a Maple PLOT data structure.\015"}}{INP_R 7 0 "> "{TEXT 0 247
 "bridge := CURVES(\012        [[0,2.9],[0,0],[10,0],[10,1],[6,3]
,[10,5],[10,6],[0,6],[0,3.1]],\012        [[6,3],[14,3]],[[10,1],
[14,3],[10,5]] ):                                                
                                                            "}}
{INP_R 8 0 "> "{TEXT 0 196 "IRtexts := TEXT( [7.5,2], `R3` ), TEX
T( [7.5,4], `R1` ), TEXT( [12.6,4], `R2` ),                      
                                              TEXT( [12.6,2], `R4
 ` ), TEXT( [10,3.2], `R5` ):"}}{INP_R 9 0 "> "{TEXT 0 173 "label
s := TEXT([10.3, 1], d), TEXT([10.3,5.2], a), TEXT([5.7,3], b), T
EXT([14.3,3], c),                                                
     TEXT([0,6.1],f),TEXT([0,-0.1],e):"}}{COM_R 10 0{TEXT 1 0 ""}
}{INP_R 11 0 "> "{TEXT 0 252 "battery := CURVES( [[-0.75,3.1], [0
.75,3.1]], [[-0.3,2.9], [0.3,2.9]] ),\012        TEXT( [1.5,3], `
It`), TEXT( [-0.3,3.3], `+`), TEXT( [-1,3], V), TEXT( [-0.3,2.7],
 `-`),                                         TEXT([9.5,3.1],`-`
), TEXT([10.5,3.1],`+`):\012"}}{INP_R 12 0 "> "{TEXT 0 126 "circu
it := PLOT( bridge, IRtexts, battery, labels,\012                
            AXESSTYLE(NONE), TITLE( `Wheatstone Bridge`) ):"}}
{INP_R 13 0 "> "{TEXT 0 49 "circuit;  # display the Wheatstone br
idge circuit"}}{COM_R 14 0{TEXT 1 174 "\015Apply Kirchhoff's rule
 for conservation of current to branch points a,b, and d, where t
he currents I1 to I5 denote respectively the currents across the 
resistors R1 to R5:\015\000"}}{INP_R 15 0 "> "{TEXT 0 17 "eqI1:=I
t-I1-I2=0;"}}{OUT_R 16 0 15{DAG :3n4\`eqI1`=3+7n3\`It`j2x0001n3\`
I1`i2x0001n3\`I2`pCj2x0000}}{INP_R 17 0 "> "{TEXT 0 17 "eqI2:=I1-
I3+I5=0;"}}{OUT_R 18 0 17{DAG :3n4\`eqI2`=3+7n3\`I1`j2x0001n3\`I3
`i2x0001n3\`I5`p8j2x0000}}{INP_R 19 0 "> "{TEXT 0 17 "eqI3:=I3+I4
-It=0;"}}{OUT_R 20 0 19{DAG :3n4\`eqI3`=3+7n3\`I3`j2x0001n3\`I4`p
8n3\`It`i2x0001j2x0000}}{COM_R 21 0{TEXT 1 206 "Apply Kirchhoff's
 rule for conservation of voltage (energy) to loops abdefa, acba 
and bcdb. Note carefully the indicated polarities of the various 
IR drops as they are encountered in each  traversing loop.\015"}}
{INP_R 22 0 "> "{TEXT 0 23 "eqV1:=-I1*R1-I3*R3+V=0;"}}{OUT_R 23 0
 22{DAG :3n4\`eqV1`=3+7*5n3\`I1`j2x0001n3\`R1`p9i2x0001*5n3\`I3`p
9n3\`R3`p9pEn3\`V`p9j2x0000}}{INP_R 24 0 "> "{TEXT 0 27 "eqV2:=-I
2*R2-I5*R5+I1*R1=0;"}}{OUT_R 25 0 24{DAG :3n4\`eqV2`=3+7*5n3\`I2`
j2x0001n3\`R2`p9i2x0001*5n3\`I5`p9n3\`R5`p9pE*5n3\`I1`p9n3\`R1`p9
p9j2x0000}}{INP_R 26 0 "> "{TEXT 0 27 "eqV3:= I5*R5-I4*R4+I3*R3=0
;"}}{OUT_R 27 0 26{DAG :3n4\`eqV3`=3+7*5n3\`I5`j2x0001n3\`R5`p9p9
*5n3\`I4`p9n3\`R4`p9i2x0001*5n3\`I3`p9n3\`R3`p9p9j2x0000}}{COM_R 
28 0{TEXT 1 45 "Solve for 6 equations in 6 unknown currents.\012"
}}{INP_R 29 0 "> "{TEXT 0 67 "sols := solve(\{eqI1,eqI2,eqI3,eqV1
,eqV2,eqV3\},\{I1,I2,I3,I4,I5,It\}):"}}{COM_R 30 0{TEXT 1 29 "\01
5Pick off the solution for I5"}}{INP_R 31 0 "> "{TEXT 0 23 "I5 :=
 subs( sols, I5 );"}}{OUT_R 32 0 31{DAG :3n3\`I5`*7n3\`V`j2x0001+
5*5n3\`R1`p6n3\`R4`p6p6*5n3\`R2`p6n3\`R3`p6i2x0001p6+11*7n3\`R5`p
6pDp6p15p6p6*7p1Dp6p12p6pAp6p6*7p1Dp6p12p6p15p6p6*7p1Dp6pDp6pAp6p
6*7p12p6pDp6p15p6p6*7p12p6pAp6p15p6p6*7pAp6pDp6p15p6p6*7p12p6pDp6
pAp6p6p18}}{COM_R 33 0{TEXT 1 118 "I5 is directly proportional to
 V.  Now find out what R4 must be to make the current I5 zero in 
terms of R1, R2, and R3"}}{INP_R 34 0 "> "{TEXT 0 16 "solve( I5, 
R4 );"}}{OUT_R 35 0 34{DAG *7n3\`R2`j2x0001n3\`R3`p3n3\`R1`i2x000
1}}{COM_R 36 0{TEXT 1 405 "which is the \"classic result\".  As p
ointed out on p.19 of Brophy's book: in the common version of a W
heatstone bridge, resistances R1 and R2  are  connected  to  a sw
itch to give decade values of the ratio R2/R1, and R3 is a contin
uously variable calibrated resistor..  Once  the  bridge  is  adj
usted such that the current I5 is zero,  then the unknown resista
nce has to be R3 R2 / R1 as shown by Maple.\012"}}}{END}
