Delmar's Standard Textbook of Electricity (MindTap Course List)
6th Edition
ISBN: 9781285852706
Author: Stephen L. Herman
Publisher: Cengage Learning
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Textbook Question
Chapter 21, Problem 4RQ
Does the current in a pure capacitive circuit lead or lag the applied voltage?
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Consider the system
dx
ax+u.
dt
Compute the exponential response of the system and use this to derive the transfer
function from u to x. Show that when s = a, a pole of the transfer function, the
response to the exponential input u(t) = est is x(t) = eat x(0) + teat.
For solving the system with u = eat
eat you can't use the
transfer function because the denominator is zero. Try
using the convolution integral solution with initial
conditions set as x(t) =
eat x (0) + fo g(t − T)u(T)dT
-
g(t) is the impulse response of the system.
dny
dn-1y
dn-1u
dn-24
+a1
+
+ Any
=
bi
+b₂-
+ +bnu.
dtn
dtn-1
dtn-1
dtn-2
a) Let be a root of the characteristic equation
1
sn+a1sn-
+
+an
= : 0.
Show that if u(t) = 0, the differential equation has the solution y(t) = e\t.
b) Let к be a zero of the polynomial
b(s) = b₁s-1+b2sn−2+
Show that if the input is u(t)
equation that is identically zero.
=
..
+bn.
ekt, then there is a solution to the differential
dny
dn-1y
dn-1u
dn-24
+a1
+
+ Any
=
bi
+b₂-
+ +bnu.
dtn
dtn-1
dtn-1
dtn-2
a) Let be a root of the characteristic equation
1
sn+a1sn-
+
+an
= : 0.
Show that if u(t) = 0, the differential equation has the solution y(t) = e\t.
b) Let к be a zero of the polynomial
b(s) = b₁s-1+b2sn−2+
Show that if the input is u(t)
equation that is identically zero.
=
..
+bn.
ekt, then there is a solution to the differential
Chapter 21 Solutions
Delmar's Standard Textbook of Electricity (MindTap Course List)
Ch. 21 - Can current flow through a capacitor?Ch. 21 - What two factors determine the capacitive...Ch. 21 - How many degrees are the current and voltage out...Ch. 21 - Does the current in a pure capacitive circuit lead...Ch. 21 - 5. A 30- capacitor is connected into a 240-V,...Ch. 21 - 6. A capacitor is connected into a 1250-V, 1000-Hz...Ch. 21 - 7. A capacitor is to be connected into a 480-V,...Ch. 21 - On the average, by what factor is the life...Ch. 21 - A capacitor is connected into a 277-V, 400-Hz...Ch. 21 - A capacitor has a voltage rating of 350 VAC. Can...
Ch. 21 - A utility company plans to connect a total of 20 F...Ch. 21 - What is the minimum AC voltage rating of each...Ch. 21 - What is the total current flow through the circuit...Ch. 21 - What is the minimum KVAR rating of each capacitor...Ch. 21 - You are working as an electrician in an industrial...Ch. 21 - You are working in an industrial plant. You have...Ch. 21 - Capacitive Circuits Fill in all the missing...Ch. 21 - A 4.7-F capacitor is connected to a 60-Hz power...Ch. 21 - A capacitor is connected to a 208-volt, 60-Hz...Ch. 21 - A 0.47-F capacitor is connected to a 240-volt...Ch. 21 - Three capacitors having capacitance values of...Ch. 21 - A capacitor has a capacitive reactance of 300 ...Ch. 21 - A pure capacitive circuit is connected to a...
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- For step a), use equations (2) to find the equation for the input impedance equations (2) are V1 = jwL1I1 + jwMI2 and V2 = jwMI1 + jwL2I2 equation for the input impedance: Z1 = V1/I1 = jwL1 + (wM)2/(jwL2 + ZL)arrow_forwardL (a) Find currents i, and b₂ 2 2 (b) Find the dependent source voltage given as Find voltages V, and (c) V₂ 5i2 (d) For each circuit element in the circuit and the two Sources, state whether they are ABSORBING OF SUPPYING Power and how much power is absorbed or Supplied. + V - 5A +lov- C/E₂ + C/E4 Vz い 5+2 + 1A C/E 5V + シュ 2A + 10Varrow_forward4) A circuit is given as shown. (a) Find currents i, and i2. (b) Find the dependent source voltage given as 5i2 (c) Find voltages V, and V₂ 2 (d) For each circuit element in the circuit and the two Sources, State whether they are ABSORBING, OF SUPPLYING POWER and how much power is absorbed or supplied. + 10V - + 4 CIES C/E + V L₁ 4 1A Y T5A GE -5V + CIES iz 2A 2 52 2 +arrow_forward
- Determine the eigenvalues and eigenvectors of using A = ( 1 -3 3 3 -5 3 6-64 Gauss eliminationarrow_forward5) A circuit is given as shown (a) Find currents i₁, L2 and is . (6) Find voltages V, V2, V3 and Vy (c) For each circuit element in the circuit and the two sources, state whether they are ABSORBING SUPPLYING POWER and how much power is absorbed or supplied. + V₁ CIE, 1A +2V- C/E AS 1A + - 4A Vy+ CES CIES 2A4 + IOV +- + + V2 1 434 12V GVarrow_forwardDetermine the eigenvalues and eigenvectors of using Gauss A = -3 322 20 132 -3° 10 -2 4 eliminationarrow_forward
- Can you please help me with this problem?arrow_forwardConsider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. + VG1( R1 1k N1:N2 11.5:1 12 V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (=V1/11) in Equations (4) of the prelab reading. Equations (2) are: V₁ = joLI₁ + jœMI₂ and V₂ = j@MI₁ +j@L₂I₂ The equation for the input impedance is: Z₁ = 1½ = jwL₁ + (WM)² jwL₂+ZL b) Assuming that Z is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms…arrow_forwardUse: R1 = 1.5K, R2 = 5K, R3 = 1K, R4 = 2K, R5 = 2K, R6 = 1K. 40%: Find the value for Vs (in V) such as IR2 = 1mA. 40%: Find the voltage VD. 20%: simulate the circuit in Falstad (attach the link). A 1,5k B R1 Vs L 5k P2 R2 R6 E C R3 С IR2= 1mA D H4 R4 2k 2k R5arrow_forward
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