Suppose that at t = 0, we connect an uncharged 10 { μ F capacitor to a charging circuit consisting of a 2500-V voltage source in series with a 2 { M Ω resistance. At t = 40 s, the capacitor is disconnected from the charging circuit and connected in parallel with a 5 { M Ω resistor. Determine the voltage across the capacitor at t = 40 s and at t = 100 s. ( Hint: You may find it convenient to redefine the time variable to be t’ = t -40 for the discharge interval so that the discharge starts at t’ = 0.)
Suppose that at t = 0, we connect an uncharged 10 { μ F capacitor to a charging circuit consisting of a 2500-V voltage source in series with a 2 { M Ω resistance. At t = 40 s, the capacitor is disconnected from the charging circuit and connected in parallel with a 5 { M Ω resistor. Determine the voltage across the capacitor at t = 40 s and at t = 100 s. ( Hint: You may find it convenient to redefine the time variable to be t’ = t -40 for the discharge interval so that the discharge starts at t’ = 0.)
Suppose that at t= 0, we connect an uncharged 10
{
μ
F
capacitor to a charging circuit consisting of a 2500-V voltage source in series with a 2
{
M
Ω
resistance. At t= 40 s, the capacitor is disconnected from the charging circuit and connected in parallel with a 5
{
M
Ω
resistor. Determine the voltage across the capacitor at t =40 s and at t= 100 s. (Hint: You may find it convenient to redefine the time variable to be t’ = t-40 for the discharge interval so that the discharge starts at t’ = 0.)
a) Write down the order of the transfer function in each of the following cases. Assume that
there are no terms in the numerator that will cancel terms in the denominator.
10
H(s)
H(s)
=
s+1
5
(s+3)(s—. 4)
4s1
5
H(s)
=
H(s)
-
83 +1
s27s
6
H(s)
H(s)
=
s(s²+4s)
2s27s+1
84583882 +3s+2
H(s)
83 +8
s+1
=
H(s)
s34s26s+5
s52s4383 + 4s2 +5s +6
Question 5 (
A system is found to have zeros of -3 and poles of 4, and -2. The system also has a gain of
4. Write out the corresponding transfer function.
Question 6.
A system has a transfer function of
What is the gain, K, of the system?
Question 7 (
A system has a transfer function of
H(s)
-
4
8+5
H(s):
=
4
8 +5
A step input of size 3 is applied to the system at time zero (Since we're dealing with transfer
functions, x(0) is also zero at time zero).
a) [10] What is the response ✗(s) of the system?
b) [10] Derive the time dependent solution, x(t), of this response
Chapter 4 Solutions
Electrical Engineering: Principles & Applications, Student Value Edition Plus Mastering Engineering with Pearson eText -- Access Card Package (7th Edition)
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