Lesson 2 - Practice Problem (KEY)

1. Convert the following numbers to engineering notation:

46500000 V 46.5MV 0.00000983 A 9.83µA 792000000000 Ω 792GΩ

6150 V 6.15kV 0.0019 A 1.9mA 20000000000 Ω 20GΩ

2. Use the decision matrix below to determine which laptop would be the best choice.

	Screen Size	Cost
Laptop A	15	$1000
Laptop B	17	$1200
Decision matrix: (assume larger screen size is desired)

Laptop	—-	Screen Size	—-	—-	Cost	—-	Total
Weight	———–	Determined in class	———–	———–	Determined in class	———–
————	Value	Norm	Weighted	Value	Norm	Weighted
A	15	0.882		1000	1.000
B	17	1.000		1200	0.833

3. Determine which house would be the best choice.

	Commute Time	Square Footage	Cost
House A	15 min	2000	$220000
House B	5 min	1500	$250000
House C	30 min	3000	$200000

Decision matrix: shorter commute time, larger square footage and lower cost are desired

House	—-	Commute time	—-	—-	Square Footage	—-	—-	Cost	—-	Total
Weight	—-	Determined in Class	—-	—-	Determined in Class	—-	—-	Determined in class
	Value	Norm	Weighted	Value	Norm	Weighted	Value	Norm	Weighted
A	15	0.333		2000	0.667		$220K	0.909
B	5	1.000		1500	0.500		$250K	0.800
c	30	0.167		3000	1.000		$200K	1.000

4. You are evaluating three different AC-to-DC converters that all meet your requirements for ripple (how much the supposed DC output actually changes) and cost. Since you want to use these devices for a scientific instrument, you really want to minimize ripple but are limited by a small budget. Use a decision matrix to choose the best one. Assume a weight of 60% for ripple and 40% for cost.

Part	Ripple	Cost
A	30mV	$20
B	35mV	$14
C	45mV	$12

Part	—-	Ripple	—-	—-	Cost	—-	Total
Weight	—-	0.6	—-	—-	0.4	—-
	Value	Norm	Weighted	Value	Norm	Weighted
A	30mV	1		0.600	$20	0.600	0.240
B	35mV	0.857	0.514	$14	0.857	0.343	0.857
C	45mV	0.667	0.400		$12	1	0.400

Part B is the best AC-to-DC Converter because it has the highest total score.

5. Three options are proposed to provide power to a new community. The cost and efficiency for each option are shown below.

Option	Cost	Efficiency
X	$3.2M	99.4%
Y	$3.0M	97.2%
Z	\2.8M	86.0%

(a) If cost and efficiency are considered equally as important, which is the better option?

Option	—-	Cost	—-	—-	Efficiency	—-	Total
Weight	—-	0.5	—-	—-	0.5	—-
	Value	Norm	Weighted	Value	Norm	Weighted
X	$3.2	0.875	0.438	99.4%	1	0.5	0.938
Y	$3.0	0.993	0.467	97.2%	0.978	0.489	0.956
Z	$2.8	1	0.5	86.0%	0.865	0.433	0.933

Part Y is the best option because it has the highest total score.

(b) If efficiency is considered 9 times as important as cost, which is the better option?

\[Weight_{cost} + Weight_{efficiency} = 1\]

\[Weight_{efficiency} = 9*Weight_{cost}\]

\[\ Weight_{cost} + 9*Weight_{cost} = 1\]

\[Weight_{cost} = \frac{1}{10} = 0.1\]

\[Weight_{efficiency} = 9*\left( \frac{1}{10} \right) = \frac{9}{10} = 0.9\]

Option	—-	Cost	—-	—-	Efficiency	—-	Total
Weight	—-	0.1	—-	—-	0.9	—-
	Value	Norm	Weighted	Value	Norm	Weighted
X	$3.2M	0.875	0.088	99.4%	1	0.9	0.988
Y	$3.0M	0.993	0.093	97.2%	0.978	0.880	0.973
Z	$2.8M	1	0.1	86.0%	0.865	0.779	0.879

Part X is the best option because it has the highest total score.

6. Convert the following in to engineering notation:

(a) 5.45 x 10^-7^ A 545 nA

(b) 123,400 W 123 kW

(c) 8.33 x 10^7^ V 83.3 MV

(d) 4.3 x 10^10^ bits (b) 43 Gb

(e) 1,497,000 Hz 1.497 MHz

(f) 76.2 x 10^-4^ m 7.62 mm

(g) 2.31 x 10^-5^ m 23.1 μm

(h) 1.78 x 10^-14^ W 17.8fW