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20.309:
Biological
Instrumentation
and
Measurement
Laboratory
Fall
2006
Homework
Set
1
Due
by
12:00
noon
on
Friday,
Sep.
22,
2006
in
16352.
1.
Figure
1
shows
a
resistor
network
known
as
a
Wheatstone
Bridge,
which
will
be
part
of
apparatus
that
you’ll
build
shortly
for
the
DNA
melting
curves
module.
You
can
read
a
bit
more
about
it
in
the
handout
for
that
module.
For
now,
we
will
look
at
it
analytically.
R
x
is
a
resistance
you
are
trying
to
measure,
and
R
3
is
a
variable
resistor.
Figure
1:
A
Wheatstone
bridge
circuit.
(a)
Assuming
R
3
is
set
such
that
the
bridge
is
balanced
(i.e.
V
ab
=
0),
derive
an
analytical
expression
for
R
x
in
terms
of
R
1
,
R
2
and
R
3
.
(b)
Now
let
R
3
also
be
a
ﬁxed
value,
and
suppose
that
R
x
varies
in
a
way
that
makes
V
ab
nonzero.
Derive
an
expression
for
the
dependence
of
V
ab
on
R
x
2.
Referring
again
to
the
Wheatstone
Bridge
in
Figure
1,
suppose
that
R
x
varies
with
some
physical
parameter
(strain,
temperature,
etc.)
in
the
range
of
110kΩ.
You
want
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 Fall '06
 MatthewLang

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