€Describing the System and Evaluating Its Performancetank B with water. Fresh water enters tank A at the rate of 8 gal/min, themixture of salt and water (assumed uniform) leaves A and enters B at therate of 8 gal/min, and the flow is incompressible. Let q(t) and p(r) bethe number of pounds of salt contained in tanks A and B, respectively.(a) Write a set of state equations for the system.(b) Draw a block diagram (or signal flow graph) for the system.(c) Find the state transition matrix ❤(t).(d) Determine g(t) and p(t) for t > 0.1-2. (a) Using the capacitor voltage v.(t) and the inductor current i(t) as states,write state equations for the RLC series circuit shown in Fig. 1-P2.PI+Rwww000i₂ (1)+Vc (1) Ce(t)Problems22tFigure 1-P241-(b) Find the state transition matrix p() if R = 3 Q2, L = 1 H, C = F.(c) If v.(0) = 0, i(0) = 0, and e(t) is as shown, determine v.(t) and i(t)for t> 0.

1-2. (a) Using the capacitor voltage v.(t) and the inductor current i(t) as states, write state equations for the RLC series circuit shown in Fig. 1-P2. + R www L i₂ (1) + Vc (1) C e(t) Figure 1-P2 4- (b) Find the state transition matrix p() if R = 3 , L = 1 H, C = F. (c) If v.(0) = 0, i(0) = 0, and e(t) is as shown, determine v.(t) and i(t) for t> 0.

1-2. (a) Using the capacitor voltage v.(t) and the inductor current i(t) as states, write state equations for the RLC series circuit shown in Fig. 1-P2. + R www L i₂ (1) + Vc (1) C e(t) Figure 1-P2 4- (b) Find the state transition matrix p() if R = 3 , L = 1 H, C = F. (c) If v.(0) = 0, i(0) = 0, and e(t) is as shown, determine v.(t) and i(t) for t> 0.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Sinusoids And Phasors

Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.

Circuit Theory

Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).

Question

€
Describing the System and Evaluating Its Performance
tank B with water. Fresh water enters tank A at the rate of 8 gal/min, the
mixture of salt and water (assumed uniform) leaves A and enters B at the
rate of 8 gal/min, and the flow is incompressible. Let q(t) and p(r) be
the number of pounds of salt contained in tanks A and B, respectively.
(a) Write a set of state equations for the system.
(b) Draw a block diagram (or signal flow graph) for the system.
(c) Find the state transition matrix ❤(t).
(d) Determine g(t) and p(t) for t > 0.
1-2. (a) Using the capacitor voltage v.(t) and the inductor current i(t) as states,
write state equations for the RLC series circuit shown in Fig. 1-P2.
PI
+
R
www
000
i₂ (1)
+
Vc (1) C
e(t)
Problems
2
2
t
Figure 1-P2
41-
(b) Find the state transition matrix p() if R = 3 Q2, L = 1 H, C = F.
(c) If v.(0) = 0, i(0) = 0, and e(t) is as shown, determine v.(t) and i(t)
for t> 0.

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