
Concept explainers
The KCL equations for a three-node circuit are as follows:
Draw the circuit diagram and indicate the reference directions for the element currents.

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Chapter 2 Solutions
EBK THE ANALYSIS AND DESIGN OF LINEAR C
- c) An RC circuit is given in Figure Q1.1, where Vi(t) and Vo(t) are the input and output voltages. (i) Derive the transfer function of the circuit. (ii) With a unit step change of Vi(t) applied to the circuit, derive the time response of Vo(t) with this step change. Vi(t) C₁ Vo(1) R₂ C2 C3 | R = 20 ΚΩ = 50 ΚΩ C=C2=C3=25 μF Figure Q1.1. RC circuit.arrow_forwardc) An RC circuit is given in Figure Q1. vi(t) and vo (t) are the input and output voltages. (i) Derive the transfer function of the circuit. (ii) With a unit step change vi(t) applied to the circuit, derive and sketch the time response of the circuit. R₁ R2 v₁(t) R3 C₁ v₁(t) R₁ = R₂ = 10 k R3 = 100 kn C₁ = 100 μF Figure Q1. RC circuit.arrow_forwardc) A RC circuit is given in Figure Q1.1. Vi(t) and Vo(t) are the input and output voltages. (i) Derive the transfer function of the circuit. (ii) With a unit step change of Vi(t) applied to the circuit, derive the time response of the circuit. C₁ C₂ Vi(t) Vo(1) R₁ C₂ R-25 k C=C2=50 µF Figure Q1.1. RC circuit.arrow_forward
- Answer 2 questions for 100 marks Question 1: Process Design [25 marks] An incomplete process design of a flash drum distillation unit is presented in Figure 1. The key variables to be controlled are flow rate, temperature, composition, pressure and liquid level in the drum. Disturbances are observed in the feed temperature and composition. Heat exchangers Drum Vapor Liquid Pump Figure 1: Incomplete process design of a distillation unit Answer the following questions briefly and in a qualitative fashion: a) Determine which sensors and final elements are required so that the important variables can be controlled. Sketch them in the figure using correct instrumentation tags. Describe briefly what instruments you will use and where they should be located. Reflect on the potential presence of a flow controller upstream of your process design (not shown in the diagram). How would this affect the level controller in the drum? b) [10 marks] Describe briefly how you qualitatively determine the…arrow_forwardAnswer 2 questions for 100 marks Question 1: Process Design [25 marks] An incomplete process design of a flash drum distillation unit is presented in Figure 1. The key variables to be controlled are flow rate, temperature, composition, pressure and liquid level in the drum. Disturbances are observed in the feed temperature and composition. Heat exchangers Drum Vapor Liquid Pump Figure 1: Incomplete process design of a distillation unit Answer the following questions briefly and in a qualitative fashion: a) Determine which sensors and final elements are required so that the important variables can be controlled. Sketch them in the figure using correct instrumentation tags. Describe briefly what instruments you will use and where they should be located. Reflect on the potential presence of a flow controller upstream of your process design (not shown in the diagram). How would this affect the level controller in the drum? b) [10 marks] Describe briefly how you qualitatively determine the…arrow_forwardQuestion 2: Process Control [75 marks] As a process engineer, you are tasked to control the process shown in Figure 2. For biomedical engineers, the process could be interpreted as the injection of a solution of a medication compound A, with initial concentration CAO, into a human body, simplified as a Continuously Stirred Tank Reactor (CSTR). Therefore, your task is to analyse and model this process. The equipment consists of a mixing tank, mixing pipe and CSTR. F₁ Сло CA2 V₁ mixing pipe F4 CA4 F3 CA3 mixing tank Fs CAS Vs stirred-tank reactor Figure 2: Mixing and reaction processes Assumptions used for modelling are as follows: I. Both tanks are well mixed and have constant volume and temperature. II. All pipes are short and contribute negligible transportation delay, III. All flow rates are constant. All densities are constant and uniform throughout. IV. The first tank is a mixing tank. V. VI. The mixing pipe has no accumulation, and the concentration CA3 is constant The second tank…arrow_forward
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