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.

	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
	Value	Norm	Weighted	Value	Norm	Weighted
A	15	0.882		1000	1.000
B	17	1.000		1200	0.833

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 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