DELMAR'S STANDARD TEXT OF ELECTRICITY
6th Edition
ISBN: 9780357323380
Author: Herman
Publisher: CENGAGE C
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Chapter 5, Problem 5RQ
A 0.5-W,
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Consider the homogeneous RLC circuit (no voltage source) shown in the diagram below. Before
the switch is closed, the capacitor has an initial charge go and the circuit has an initial current go-
R
9(1)
i(t)↓
After the switches closes, current flows through the circuit and the capacitor begins to discharge.
The equation that describes the total voltage in the loop comes from Kirchoff's voltage law:
L
di(t)
+ Ri(t)+(0) = 0,
(1)
where i(t) and q(t) are the current and capacitor charge as a function of time, L is the inductance,
R is the resistance, and C is the capacitance. Using the fact that the current equals the rate of
change of the capacitor charge, and dividing by L, we can write the following homogeneous (no
input source) differential equation for the charge on the capacitor:
4(1) +29(1)+w79(1)=0,
ཀྱི
where
a=
R
2L
and
The solution to this second order linear differential equation can be written as:
9(1) =Aent - Beat,
where
(3)
(4)
(5)
A=
(81+20)90 +90
(82+20)90 +90
and B=
(6)…
Consider the homogeneous RLC circuit (no voltage source) shown in the diagram below. Before
the switch is closed, the capacitor has an initial charge go and the circuit has an initial current go.
R
w
i(t)
q(t)
C
н
After the switches closes, current flows through the circuit and the capacitor begins to discharge.
The equation that describes the total voltage in the loop comes from Kirchoff's voltage law:
di(t)
L
+ Ri(t) + (t) = 0,
dt
(1)
where i(t) and q(t) are the current and capacitor charge as a function of time, L is the inductance,
R is the resistance, and C is the capacitance. Using the fact that the current equals the rate of
change of the capacitor charge, and dividing by L, we can write the following homogeneous (no
input source) differential equation for the charge on the capacitor:
ä(t)+2ag(t)+wg(t) = 0,
(2)
where
R
a
2L
and w₁ = C
LC
The solution to this second order linear differential equation can be written as:
where
81=
q(t) = Ae³¹- Bel
82 =
(3)
(4)
(5)
I need help with this problem and an explanation of the solution for the image described below. (Introduction to Signals and Systems)
Chapter 5 Solutions
DELMAR'S STANDARD TEXT OF ELECTRICITY
Ch. 5 - Name three types of fixed resistors.Ch. 5 - What is the advantage of a metal film resistor...Ch. 5 - What is the advantage of a wire-wound resistor?Ch. 5 - How should tubular wire-wound resistors be mounted...Ch. 5 - A 0.5-W, 2000- resistor has a current flow of 0.01...Ch. 5 - A 1-W, 350- resistor is connected to 24 V. Is this...Ch. 5 - A resistor has color bands of orange, blue,...Ch. 5 - A 10,000- resistor has a tolerance of 5%. What are...Ch. 5 - Is 51,000 a standard value for a 5% resistor?Ch. 5 - What is a potentiometer?
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- SOLVE ON PAPER DO NOT USE CHATGPT OR AIarrow_forwardA particular battery charger produces a constant current of 2.4 amperes to charge a 3.7 volt Iphone battery. It can fully charge a dead battery to full charge in 6 hours. (a) What amp-hour charge is stored in the charged battery? (b) How many coulombs does the charge battery hold? (c) Can the fully charged battery continuously operate a phone that needs 0.25 amperes of current for a 24 hour period of time?arrow_forwardDesign 5th order LPF with gain = Yo cut of freq=10KHZarrow_forward
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