Practice Problems (KEY)

Problem 1

Convert the following numbers to engineering notation:

• 46500000 V → 46.5 MV

• 0.00000983 A → 9.83 µA

• 792000000000 Ω → 792 GΩ

• 6150 V → 6.15 kV   0.0019 A → 1.9 mA

• 20000000000 Ω → 20 GΩ

Problem 2

Use the decision matrix below to determine which laptop would be the best choice. The weights for screen size and cost will be determined in class.

	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

The weights are determined in class, so the Weighted and Total cells are intentionally left blank. Once the class has chosen weights that sum to 1.0, multiply each normalized score by its weight and add the two weighted scores for each laptop; the laptop with the highest total score is the best choice.

Problem 3

Determine which house would be the best choice.

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

Problem 4

Part	Ripple			Cost			Total
Weight		0.6			0.4
	Value	Norm	Weighted	Value	Norm	Weighted
A	30 mV	1.000	0.600	$20	0.600	0.240	0.840
B	35 mV	0.857	0.514	$14	0.857	0.343	0.857
C	45 mV	0.667	0.400	$12	1.000	0.400	0.800

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

Problem 5

(a) Cost and efficiency weighted equally (0.5 each):

Option	Cost			Efficiency			Total
Weight		0.5			0.5
	Value	Norm	Weighted	Value	Norm	Weighted
X	$3.2M	0.875	0.438	99.4%	1.000	0.500	0.938
Y	$3.0M	0.933	0.467	97.2%	0.978	0.489	0.956
Z	$2.8M	1.000	0.500	86.0%	0.865	0.433	0.933

Option Y is the best because it has the highest total score.

(b) Efficiency 9× more important than cost:

\[W_{cost} + W_{efficiency} = 1, \qquad W_{efficiency} = 9 W_{cost}\]

\[W_{cost} = 0.1, \qquad W_{efficiency} = 0.9\]

Option	Cost			Efficiency			Total
Weight		0.1			0.9
	Value	Norm	Weighted	Value	Norm	Weighted
X	$3.2M	0.875	0.088	99.4%	1.000	0.900	0.988
Y	$3.0M	0.933	0.093	97.2%	0.978	0.880	0.973
Z	$2.8M	1.000	0.100	86.0%	0.865	0.779	0.879

Option X is the best because it has the highest total score.

Problem 6

(a) 5.45 × 10⁻⁷ A → 545 nA
(b) 123,400 W → 123.4 kW
(c) 8.33 × 10⁷ V → 83.3 MV
(d) 4.3 × 10¹⁰ bits → 43 Gb
(e) 1,497,000 Hz → 1.497 MHz
(f) 76.2 × 10⁻⁴ m → 7.62 mm
(g) 2.31 × 10⁻⁵ m → 23.1 µm
(h) 1.78 × 10⁻¹⁴ W → 17.8 fW