(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function, i. Calculate the time constant t. ii. iii. Calculate ve(t) at t = ∞o. Obtain an expression for vċ(t) valid for all values of t.
(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function, i. Calculate the time constant t. ii. iii. Calculate ve(t) at t = ∞o. Obtain an expression for vċ(t) valid for all values of t.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function,
i. Calculate the time constant T.
ii.
iii.
iv.
Calculate ve(t) at t = ∞o.
Obtain an expression for vċ(t) valid for all values of t.
Calculate the total energy stored in the capacitor at t = 6 ms.
4u(t) V
3 kQ2
1kΩ.
Figure Q2-2
4 μF
+
VC](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08328c9e-758c-4124-82a6-87487ac7cf48%2Ff2cd8cfb-3967-42c9-b558-3b9b6fc108c0%2Fwzw1sil_processed.png&w=3840&q=75)
Transcribed Image Text:(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function,
i. Calculate the time constant T.
ii.
iii.
iv.
Calculate ve(t) at t = ∞o.
Obtain an expression for vċ(t) valid for all values of t.
Calculate the total energy stored in the capacitor at t = 6 ms.
4u(t) V
3 kQ2
1kΩ.
Figure Q2-2
4 μF
+
VC
![Table 1: Laplace Transform Properties
Linearity L {af(t)} = aF(s)
Superposition
Modulation L {e-at f(t)} = F(s + a)
Time-Shifting L{f(t-7)u(t-7)} = e-TF(s)
Scaling L{f(at)} = F(2)
| L { $(10)} = 8
= 8F(s)-f(0)
L{f(t)} = F(s)
L {fi(t) + f₂(t)} = F₁(s) + F₂(s)
Real Differentiation L
Real Integration
Complex Differentiation
L {tf(t)}
-F(s)
ds
Complex Integration {f} = f* F(®)
L
Convolution L {f(t) *g(t)} = F(s). G(s)
Table 2: Common Laplace Transform Pairs
f(t)
F(s)
8(t)
u(t)
tu(t)
e-atu(t)
te-atu(t)
cos(wt)u(t)
sin(wt)u(t)
1
1
s+a
1
(s + a)²
8
8² +w²
8² +w²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08328c9e-758c-4124-82a6-87487ac7cf48%2Ff2cd8cfb-3967-42c9-b558-3b9b6fc108c0%2F8nrtgju_processed.png&w=3840&q=75)
Transcribed Image Text:Table 1: Laplace Transform Properties
Linearity L {af(t)} = aF(s)
Superposition
Modulation L {e-at f(t)} = F(s + a)
Time-Shifting L{f(t-7)u(t-7)} = e-TF(s)
Scaling L{f(at)} = F(2)
| L { $(10)} = 8
= 8F(s)-f(0)
L{f(t)} = F(s)
L {fi(t) + f₂(t)} = F₁(s) + F₂(s)
Real Differentiation L
Real Integration
Complex Differentiation
L {tf(t)}
-F(s)
ds
Complex Integration {f} = f* F(®)
L
Convolution L {f(t) *g(t)} = F(s). G(s)
Table 2: Common Laplace Transform Pairs
f(t)
F(s)
8(t)
u(t)
tu(t)
e-atu(t)
te-atu(t)
cos(wt)u(t)
sin(wt)u(t)
1
1
s+a
1
(s + a)²
8
8² +w²
8² +w²
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