Principles Of Electric Circuits
10th Edition
ISBN: 9780134879482
Author: Floyd, Thomas L.
Publisher: Pearson,
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Textbook Question
Chapter 1, Problem 18RP
How would you show the number 10,000 showing three significant digits?
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Calculate the resistance for Aluminum wire, 8 AWG with a length of 1000 FT*
Introduction
The circuit of Fig. 1 is required to be modeled using a state - space representation, where 2
states will be used, based on the number of the energy - storing elements of the circuit, the
capacitor and the inductor.
u(t)
+
ΙΩ
www
13
F
5 Ω it (t)
www
vc(t) 1 H
Figure 1: LCR circuit
The input signal to the circuit is the voltage u(t) in Volts and the output signal is the voltage
across the capacitor, vc(t).
Questions
1. Choice of system states:
Choose appropriate signals for the 2 states of the
system.
x₁(t) = i₁(t)
x₂ (t) =
5. State transition matrix:
(t), which is defined as,
Calculate analytically the state transition matrix
(t) = et = L¯¹{(sI – A)¯¹}
Show that the answer is the following,
1
e-4t cos(√2t) -
e-4 sin(√2 t)
1
e
-4t
√2
(t) = et
-3
1
-4t sin (√2 t)
e
COS
-4t cos (√2t) + -
e
sin(√2 t)
2-4t sin(√2 t)|
Calculate the following:
(SI - A)-1=
Use the completion - in - the-square technique (CASE 3) to calculate the inverse Laplace:
L¯¹{(SI - A)¯¹} =
Chapter 1 Solutions
Principles Of Electric Circuits
Ch. 1 - Express 4,750 in scientific notation.Ch. 1 - Express 0.00738 in scientific notation.Ch. 1 - Express 9.12 103 as a regular decimal number.Ch. 1 - Add 3.1 103 and 5.5 104.Ch. 1 - Subtract 3.5 106 from 2.2 105.Ch. 1 - Multiply 3.2 106 and 1.5 103.Ch. 1 - Divide 8 106 by 2 1010.Ch. 1 - Express 36,000,000,000 in engineering notation.Ch. 1 - Express 0.0000000000056 in engineering notation.Ch. 1 - Express using metric prefixes: 1. 56,000 2....
Ch. 1 - Convert 1 mA to microamperes.Ch. 1 - Convert 1,000 mV to millivolts.Ch. 1 - Convert 893 nA to microamperes.Ch. 1 - Convert 10,000 pF to microfarads.Ch. 1 - Convert 0.0022 mF to picofarads.Ch. 1 - Convert 2.2 k to megohms.Ch. 1 - Add 2,873 mA to 10,000 mA; express the sum in...Ch. 1 - How would you show the number 10,000 showing three...Ch. 1 - What is the difference between a measured quantity...Ch. 1 - Round 3.2850 to three significant digits using the...Ch. 1 - Derived units in the SI system use base units in...Ch. 1 - The base electrical unit in the SI system is the...Ch. 1 - The supplementary SI units are for angular...Ch. 1 - The number 3,300 is written as 3.3 103 in both...Ch. 1 - A negative number that is expressed in scientific...Ch. 1 - When you multiply two numbers written in...Ch. 1 - When you divide two numbers written in scientific...Ch. 1 - The metric prefix micro has an equivalent power of...Ch. 1 - To express 56 106 with a metric prefix, the...Ch. 1 - 0.047 F is equal to 47 nFCh. 1 - 0.010 F is equal to 10,000 pF.Ch. 1 - 10,000 kW is equal to 1 MW.Ch. 1 - The number of significant digits in the number...Ch. 1 - To express 10,000 with three significant figures,...Ch. 1 - When you apply the round-to-even rule to round off...Ch. 1 - If a series of measurements are precise, they must...Ch. 1 - The base SI electrical unit is the ampere.Ch. 1 - Which of the following is not an electrical...Ch. 1 - The unit of current is a. volt b. watt c. ampere...Ch. 1 - The number of base units in the SI system is a. 3...Ch. 1 - An mks measurement unit is one that a. can be...Ch. 1 - In the Sl system, the prefix k means to multiply...Ch. 1 - Prob. 6STCh. 1 - The quantity 4.7 103 is the same as a) 470 b)...Ch. 1 - The quantity 56 103 is the same as a. 0.056 b....Ch. 1 - Prob. 9STCh. 1 - Ten milliamperes can be expressed as a. 10 MA b....Ch. 1 - Five thousand volts can be expressed as a. 5,000 V...Ch. 1 - Twenty million ohms can be expressed as a. 20 m b....Ch. 1 - Prob. 13STCh. 1 - When reporting a measured value, it is okay to...Ch. 1 - Express each of the following numbers in...Ch. 1 - Express each fractional number in scientific...Ch. 1 - Express each of the following numbers in...Ch. 1 - Express each of the following numbers in...Ch. 1 - Express each of the following numbers in...Ch. 1 - Express each of the following as a regular decimal...Ch. 1 - Express each of the following as a regular decimal...Ch. 1 - Express each number in regular decimal form: a....Ch. 1 - Add the following numbers: a. (9.2 106) + (3.4 ...Ch. 1 - Prob. 10PCh. 1 - Perform the following multiplications: a. (5 ...Ch. 1 - Prob. 12PCh. 1 - Perform the indicated operations: a. (8 104 + 4 ...Ch. 1 - Starting with 1012, list the powers of ten in...Ch. 1 - Express each of the following numbers in...Ch. 1 - Express each number in engineering notation: a....Ch. 1 - Express each number in engineering notation: a....Ch. 1 - Express each number in engineering notation: a....Ch. 1 - Add the following numbers and express each result...Ch. 1 - Multiply the following numbers and express each...Ch. 1 - Divide the following numbers and express each...Ch. 1 - Express each number in Problem 15 in ohms using a...Ch. 1 - Express each number in Problem 17 in amperes using...Ch. 1 - Express each of the following as a quantity having...Ch. 1 - Express the following using metric prefixes: a. 3 ...Ch. 1 - Express the following using metric prefixes: a....Ch. 1 - Express each quantity by converting the metric...Ch. 1 - Express each quantity in engineering notation: a....Ch. 1 - Perform the indicated conversions: a. 5 mA to...Ch. 1 - Determine the following: a. The number of...Ch. 1 - Add the following quantities: a. 50 mA + 680 A b....Ch. 1 - Do the following operations: a. 10 k (2.2 k + 10...Ch. 1 - How many significant digits are in each of the...Ch. 1 - Round each of the following numbers to three...
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