PROBLEM 5.9
KNOWN:
Four resistors are available: two rated at R = 500
±
50
Ω
and two
rated at R = 2000
±
5%
Ω
.
FIND:
Best design combination to form R
T
= 1000
Ω
SOLUTION
We can combine the resistors in series or in parallel. Consider as Case 1, a series
arrangement and as Case 2, a parallel arrangement.
Case 1
R
T
= R
1
+ R
2
If we use the two 500
Ω
resistors, then
1
R
d
u
=
±
50
Ω
2
R
d
u
=
±
50
Ω
The propagation of uncertainty through to R
T
is estimated by
1
2
2
2 1/ 2
1
2
(
)
[(
)
(
) ]
T
R
R
T
T
d
R
d
d
R
R
u
u
u
R
R
∂
∂
= ±
+
∂
∂
=
1
2
2
2
[(1*
)
(1*
)
R
R
d
d
u
u
±
+
=
71
±
Ω
(95%)
Case 2
1
2
1
2
T
R R
R
R
R
=
+
If we use the two 2000
Ω
resistors, then
1
R
d
u
=
±
100
Ω
2
R
d
u
=
±
100
Ω
The propagation of uncertainty through to R
T
is estimated by
1
2
2
2 1/ 2
1
2
(
)
[(
)
(
) ]
T
R
R
T
T
d
R
d
d
R
R
u
u
u
R
R
∂
∂
= ±
+
∂
∂
=
1
2
2
2 1/ 2
2
1
2
1
1
2
2
2
1
2
1
2
1
2
1
2
[({
}*
)
({
}*
) ]
(
)
(
)
R
R
d
d
R
R R
R
R R
u
u
R
R
R
R
R
R
R
R
±

+

+
+
+
+
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document