Simulink Step-by-Step Guide for Solving Electrical Circuit Problem

ekanshkhullar9 wrote:

(...) and what specific issue are you facing?
uses the circuit switch from two configured position and it is asking current expression
AI: What is your experience level with Simulink? Are you a beginner, or do you have some experience using it?
u can take me as an beginer only have done couple times before

To solve this problem, we need to find the current expression for the given circuit involving a switch moving from Position 1 to Position 2 at $ t = 0 $. This includes both deriving the analytical solution and simulating the behavior in Simulink. The circuit contains resistors, a DC voltage source, and an inductor.

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Step 1: Analyze the Circuit Mathematically

Given Circuit:
- Position 1: The circuit is a loop with a 20 V source, a 5 Ω resistor, and a 0.5 H inductor.
- Position 2: The circuit consists of a 40 V source, a 2 Ω resistor, and the inductor.

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Step 1.1: Solve for Initial Current ($ I(0^-) $)
1. When the circuit is in Position 1, the inductor behaves as a short circuit at steady-state (after a long time, $ t \to \infty $).
2. Using Ohm's Law, the steady-state current through the inductor is:
$$ I(0^-) = \frac{\text{Voltage}}{\text{Resistance}} = \frac{20 \, \text{V}}{5 \, \Omega} = 4 \, \text{A}. $$

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Step 1.2: Write Differential Equation for Position 2 (for $ t \geq 0 $)
1. At $ t = 0 $, the switch moves to Position 2. The circuit now includes the 40 V source, the 2 Ω resistor, and the 0.5 H inductor.
2. Using Kirchhoff's Voltage Law (KVL):
$$ 40 - L \frac{dI(t)}{dt} - R I(t) = 0, $$
where:
- $ L = 0.5 \, \text{H} $,
- $ R = 2 \, \Omega $.

3. This simplifies to:
$$ \frac{dI(t)}{dt} + 4I(t) = 80. $$

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Step 1.3: Solve the Differential Equation
1. The general solution of the first-order linear differential equation:
$$ I(t) = I_h(t) + I_p(t), $$
where:
- $ I_h(t) $ is the homogeneous solution,
- $ I_p(t) $ is the particular solution.

2. Solve the homogeneous equation:
$$ \frac{dI_h(t)}{dt} + 4I_h(t) = 0. $$
Solution:
$$ I_h(t) = C_1 e^{-4t}, $$
where $ C_1 $ is a constant.

3. Solve the particular equation:
Assuming $ I_p(t) = A $ (a constant):
$$ 4A = 80 \implies A = 20. $$

4. Combine solutions:
$$ I(t) = C_1 e^{-4t} + 20. $$

5. Find $ C_1 $ using the initial condition at $ t = 0 $:
- At $ t = 0 $, $ I(0) = I(0^-) = 4 \, \text{A} $.
$$ 4 = C_1 e^0 + 20 \implies C_1 = -16. $$

6. Final expression for the current:
$$ I(t) = -16 e^{-4t} + 20, \quad t \geq 0. $$

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Step 2: Simulate in Simulink

Now that we have the current expression, we can simulate this behavior step-by-step in Simulink.

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Step 2.1: Set Up the Model

1. Open MATLAB and Simulink:
- Type `simulink` in the MATLAB Command Window and create a new blank model.

2. Add Components:
- From the Simulink Library Browser, navigate to `Simscape > Electrical > Specialized Power Systems > Fundamentals`.
- Drag and drop the following blocks:
- Voltage Source
- Resistor
- Inductor
- Switch
- Ground

3. Add Sensors and Analysis Tools:
- Navigate to `Simscape > Electrical > Specialized Power Systems > Sensors and Measurements`.
- Add:
- A Current Measurement block (to measure the inductor current),
- A Scope block (to visualize the current waveform).

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Step 2.2: Configure Components

1. Voltage Sources:
- Set one source to 20 V (Position 1) and the other to 40 V (Position 2).

2. Resistors:
- Set one resistor to $ 5 \, \Omega $ and the other to $ 2 \, \Omega $.

3. Inductor:
- Set the inductance to $ 0.5 \, \text{H} $.

4. Switch:
- Use a Step Block from the `Simulink > Sources` library to control the switch position.
- Configure the Step Block:
- Step Time: $ 0 \, \text{s} $,
- Initial Value (Position 1): Connect to 20 V source and 5 Ω resistor,
- Final Value (Position 2): Connect to 40 V source and 2 Ω resistor.

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Step 2.3: Connect Components

1. Make connections according to the circuit diagram:
- Position 1: Voltage Source (20 V) → Resistor (5 Ω) → Inductor (0.5 H) → Ground.
- Position 2 (via switch): Voltage Source (40 V) → Resistor (2 Ω) → Inductor (0.5 H) → Ground.

2. Add the Current Measurement block in series with the inductor to measure the current.

3. Add the Scope block to the output of the Current Measurement block.

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Step 2.4: Configure Simulation Parameters

1. Go to `Simulation > Model Configuration Parameters`.
2. Set the simulation time to a few seconds (e.g., $ 5 \, \text{s} $).
3. Choose the appropriate solver:
- Use an ODE23tb or another stiff solver for accurate results.

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Step 2.5: Run the Simulation

1. Click the Run button to simulate the circuit.
2. Open the Scope block to view the inductor current waveform.

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Step 3: Verify the Results

1. The waveform displayed in the Scope should match the analytical solution:
$$ I(t) = -16 e^{-4t} + 20 \, (\text{A}). $$
2. At $ t = 0 $, the initial current is 4 A.
3. As $ t \to \infty $, the current approaches the steady-state value of 20 A.

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Conclusion

By using both mathematical analysis and Simulink simulation, we confirm the behavior of the circuit when the switch moves from Position 1 to Position 2. This workflow demonstrates how to approach transient circuit problems effectively.

Let me know if you need further assistance with the Simulink model or additional clarifications!

ekanshkhullar9 wrote:

how do i setup the step block part as well as name of step bloack exact

To set up the Step block in Simulink and control the switch in your circuit, follow these detailed instructions. This will guide you through identifying the exact block, configuring it, and integrating it into your model to simulate the switching action at $ t = 0 $.

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1. Identifying the Step Block

The exact name of the block is the "Step" block. It can be found in the Simulink Library under:



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2. Adding the Step Block to Your Model

1. Open the Simulink Library Browser:

- In your Simulink model, click the Library Browser icon or type `simulink` in the MATLAB Command Window.

2. Navigate to the Step Block:

- In the Library Browser, expand the `Simulink` category.
- Select `Sources`.
- Locate the Step block in the list.

3. Insert the Step Block:

- Drag and drop the Step block into your model workspace.

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3. Configuring the Step Block Parameters

Double-click the Step block in your model to open its parameters dialog. Set the following parameters:

- Step time: `0`
*(This is when the switch transitions from Position 1 to Position 2.)*

- Initial value: `0`
*(The output before the step time, representing Position 1 active.)*

- Final value: `1`
*(The output after the step time, activating Position 2.)*

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4. Connecting the Step Block to Control the Switch

4.1. Selecting the Appropriate Switch Component

For electrical circuits in Simulink, especially when using Simscape Electrical, you need to use switch components that handle physical connections:

- Ideal Switch
- Controlled Switch
- Breaker

These are located under:



Note: Do not use the basic Simulink "Switch" block, as it is designed for signal routing and not suitable for physical electrical circuits.

4.2. Adding the Switch to Your Model

1. Add the Switch Component:

- In the Library Browser, navigate to `Simscape > Electrical > Specialized Power Systems > Switches`.
- Drag the Ideal Switch (or Controlled Switch) into your model.

2. Insert the Switch into Your Circuit:

- Place the switch where the circuit transitions between Position 1 and Position 2.
- Ensure the switch connects the correct components for each position.

4.3. Connecting the Step Block to the Switch

1. Control Signal Connection:

- The Ideal Switch has a control input port (usually labeled "g" or similar).

2. Wire the Step Block to the Switch Control Port:

- Connect the output of the Step block to the control input of the switch.

3. Switch Operation:

- Before $ t = 0 $: Step output is `0`, switch is open or closed based on switch configuration.
- After $ t = 0 $: Step output changes to `1`, causing the switch to change state.

4.4. Configuring the Switch Parameters

- Threshold Voltage:

- Check the switch's control signal threshold in its parameters.
- The switch changes state when the control voltage crosses this threshold.

- Initial State:

- Ensure the switch's initial state corresponds to Position 1.
- You may need to adjust the Initial state parameter or invert the control signal.

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5. Setting Up the Circuit Configurations

Model both circuit positions within your Simulink model:

5.1. Position 1 (Before $ t = 0 $)

- Components:

- 20 V voltage source
- 5 Ω resistor
- 0.5 H inductor

- Connection:

- Arrange these components in series.
- This path is active when the switch is in Position 1.

5.2. Position 2 (After $ t = 0 $)

- Components:

- 40 V voltage source
- 2 Ω resistor
- Same 0.5 H inductor

- Connection:

- These components form the second path.
- Activated when the switch transitions to Position 2.

5.3. Managing Circuit Paths

- Use additional switches if needed to isolate each circuit path correctly.
- Control all switches using the Step block output or appropriate logical operations.

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6. Ensuring Correct Simulation Setup

6.1. Solver Configuration

- Choose an Appropriate Solver:

- Go to `Simulation > Model Configuration Parameters`.
- Select a solver suitable for stiff systems, such as ode23tb.

- Set Simulation Time:

- Ensure the simulation time covers the period of interest (e.g., `0` to `5` seconds).

6.2. Initial Conditions

- Inductor Initial Current:

- Set the inductor's initial current to match the pre-step steady-state current.
- Double-click the Inductor block and set Initial current to `4 A`.

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7. Verifying the Simulation Results

1. Add Measurement Blocks:

- Insert a Current Measurement block in series with the inductor.
- Connect the measurement output to a Scope or Display block.

2. Run the Simulation:

- Click the Run button in the Simulink toolbar.

3. Observe the Inductor Current:

- Open the Scope to view the inductor current over time.
- Verify that the current transitions from `4 A` to the new steady-state following the expression:

$$ I(t) = -16 e^{-4t} + 20 \, \text{A}, \quad t \geq 0 $$

4. Compare with Analytical Solution:

- Ensure the simulation results match the expected analytical behavior.

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8. Additional Considerations

8.1. Handling Switching Transients

- Snubber Circuits:

- If you encounter simulation issues due to switching transients, consider adding snubber circuits across the switch.

- Solver Tolerances:

- Adjust the solver tolerances in the configuration parameters to improve accuracy.

8.2. Signal Inversion (If Necessary)

- If the switch operates opposite to the desired behavior, invert the control signal:

- Use a Math Function block set to "u * -1".
- Alternatively, use a Logical NOT block if working with logical signals.

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Summary

- Step Block:

- Name: Step
- Location: `Simulink > Sources > Step`
- Purpose: Generates a control signal that changes from `0` to `1` at $ t = 0 $.

- Switch Control:

- Use the Step block output to control an Ideal Switch from Simscape Electrical.
- Ensure the switch correctly toggles between the two circuit configurations.

- Circuit Simulation:

- Model both circuit positions accurately.
- Set initial conditions and solver settings appropriately.

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By following these steps, you'll be able to set up the Step block and integrate it into your Simulink model to simulate the switching action at $ t = 0 $. This will allow you to observe the transient response of the circuit and validate it against the analytical solution.

Feel free to ask if you need further clarification or assistance with specific steps.

ekanshkhullar9 wrote:

can u give me a circuit diagram too or something showing how to connect the circuit

Certainly! I will provide a detailed circuit diagram and explain how to connect the components both in the physical circuit and within Simulink. This will help you visualize the circuit and guide you in creating the simulation model.

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Circuit Diagram and Connections

Overview

The circuit involves a switch that moves from Position 1 to Position 2 at time $ t = 0 $. The components in each position are as follows:

- Position 1 (for $ t < 0 $):
- Voltage Source: 20 V DC
- Resistor: 5 Ω
- Inductor: 0.5 H

- Position 2 (for $ t \geq 0 $):
- Voltage Source: 40 V DC
- Resistor: 2 Ω
- Inductor: 0.5 H (same inductor as in Position 1)

Circuit Connections

Position 1 (Before $ t = 0 $)

In Position 1, the circuit is connected as follows:

1. Positive terminal of the 20 V voltage source connects to one end of the 5 Ω resistor.
2. Other end of the 5 Ω resistor connects to one end of the 0.5 H inductor.
3. Other end of the inductor connects to the negative terminal of the 20 V voltage source (completing the loop).

This forms a simple series circuit:



Position 2 (After $ t = 0 $)

In Position 2, after the switch moves, the circuit is connected as:

1. Positive terminal of the 40 V voltage source connects to one end of the 2 Ω resistor.
2. Other end of the 2 Ω resistor connects to one end of the 0.5 H inductor.
3. Other end of the inductor connects to the negative terminal of the 40 V voltage source.

Again, forming a series circuit:



Switching Mechanism

The switch controls which voltage source and resistor are connected with the inductor:

- Before $ t = 0 $: Switch connects the 20 V source and 5 Ω resistor to the inductor.
- At $ t = 0 $: Switch moves to connect the 40 V source and 2 Ω resistor to the inductor.

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Implementing the Circuit in Simulink

Below is a step-by-step guide to creating and connecting the circuit in Simulink.

Step 1: Open Simulink and Create a New Model

- Open MATLAB.
- In the Command Window, type `simulink` and press Enter.
- In the Simulink Start Page, select Blank Model.

Step 2: Add Necessary Components

From the Simulink Library Browser, add the following components:

1. Voltage Sources:
- Locate DC Voltage Source under:

- Add two instances:
- Voltage Source 1: For 20 V.
- Voltage Source 2: For 40 V.

2. Resistors:
- Use Series RLC Branch blocks under:

- Add two instances:
- Resistor 1: Set as a resistor with R = 5 Ω.
- Resistor 2: Set as a resistor with R = 2 Ω.
- Configure each by setting L = 0 H, C = ∞ F (or 0 F if ∞ is not accepted).

3. Inductor:
- Use another Series RLC Branch block for the inductor.
- Set R = 0 Ω, L = 0.5 H, C = ∞ F.

4. Ideal Switch:
- Find Ideal Switch under:

- This will act as the control between Position 1 and Position 2.

5. Step Block:
- Under:

- Add a Step block to control the switch operation.

6. Current Measurement:
- Find Current Measurement under:

- This measures the current through the inductor.

7. Scope:
- Under:

- Add a Scope block to display the current waveform.

8. Ground and Powergui:
- Add a Ground block from:

- Add a Powergui block from:

- The Powergui is essential for simulating electrical systems.

Step 3: Configure Components

1. Voltage Sources:
- Voltage Source 1: Double-click and set Amplitude to `20 V`.
- Voltage Source 2: Set Amplitude to `40 V`.

2. Resistors:
- Resistor 1: Set R = 5 Ω, L = 0 H, C = ∞ F.
- Resistor 2: Set R = 2 Ω, L = 0 H, C = ∞ F.

3. Inductor:
- Set R = 0 Ω, L = 0.5 H, C = ∞ F.

4. Ideal Switch:
- Ensure default settings are suitable.
- The switch will be controlled by the voltage from the Step block.

5. Step Block:
- Set Step time to `0`.
- Set Initial value to `0`.
- Set Final value to `1`.

6. Inductor Initial Current:
- To set the initial current of the inductor, you may need to initialize the simulation state:
- In the Powergui block, select Preferences > Initial States Setting.
- Set the initial current in the inductor to `4 A` (steady-state current before switch changes).

Step 4: Connect Components

1. Position 1 Circuit:

- Voltage Source 1 positive terminal to one end of Resistor 1.
- Other end of Resistor 1 to Terminal 1 of the Ideal Switch.
- Negative terminal of Voltage Source 1 to Ground.

2. Position 2 Circuit:

- Voltage Source 2 positive terminal to one end of Resistor 2.
- Other end of Resistor 2 to Terminal 2 of the Ideal Switch.
- Negative terminal of Voltage Source 2 to Ground.

3. Switch Common Connection:

- Common Terminal of the Ideal Switch to one end of the Inductor.
- Other end of the Inductor to Ground.

4. Current Measurement:

- Insert Current Measurement block between the Ideal Switch Common Terminal and the Inductor.

5. Scope:

- Connect output of the Current Measurement block to the Scope.

6. Step Control Signal:

- Connect the output of the Step block to the control input of the Ideal Switch.

7. Grounding:

- Ensure all ground connections are made via the Ground block.

Step 5: Configure Simulation Parameters

1. Solver Configuration:

- Open Simulation > Model Configuration Parameters.
- In the Solver tab:
- Set Start time to `0`.
- Set Stop time to `5` seconds (or longer to observe steady-state).
- Choose Type as Fixed-step or Variable-step.
- For variable-step, select Solver as ode23tb (stiff/TR-BDF2).

2. Powergui:

- Ensure the Powergui block is present in the model.
- It should be set to Continuous or Discrete modes depending on your simulation requirements.

Step 6: Run the Simulation

- Click the Run button (green play icon) in the Simulink toolbar.
- Open the Scope to observe the inductor current waveform over time.

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Supporting Details and Explanations

Understanding the Switching Mechanism

- Before $ t = 0 $:
- The Step block outputs `0`, keeping the Ideal Switch connected to Terminal 1.
- The circuit consists of the 20 V source, 5 Ω resistor, and 0.5 H inductor.

- After $ t = 0 $:
- The Step block outputs `1`, causing the Ideal Switch to connect to Terminal 2.
- The circuit now consists of the 40 V source, 2 Ω resistor, and the same inductor.

Initial Conditions

- Setting the inductor's initial current to `4 A` is crucial, as it reflects the steady-state current from Position 1 before the switch transitions.
- This ensures the simulation accurately represents the inductor's behavior during the switching event.

Expected Results

- The current through the inductor should follow the expression:

$$ I(t) = -16 e^{-4t} + 20 \, \text{A}, \quad t \geq 0 $$

- At $ t = 0 $, $ I(0) = 4\,\text{A} $.
- As $ t \to \infty $, $ I(t) \to 20\,\text{A} $, the steady-state current with the 40 V source and 2 Ω resistor.

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Caveats and Additional Considerations

1. Switch Configuration:

- If the switch does not operate as expected, verify the control signal and the Threshold parameter in the Ideal Switch.
- You may need to adjust the Initial value and Final value in the Step block or use a Relational Operator block to adjust the control logic.

2. Solver Settings:

- For accurate simulation of switching events, using a stiff solver like ode23tb is recommended.
- If the simulation is slow or shows errors, try adjusting the Max step size or tolerances in the solver settings.

3. Component Libraries:

- Ensure all components are from the Simscape Electrical Specialized Power Systems library for compatibility.

4. Simulation Time:

- Extend the Stop time if you wish to observe the circuit's behavior over a longer period.

5. Measurement Units:

- Consistency in units is crucial. Ensure all parameters use SI units (Volts, Ohms, Henrys, etc.).

6. Visualization:

- You can add Display or Numerical blocks to monitor values at specific points.
- Use the Signal Logging feature for more detailed analysis.

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Summary

You now have a detailed description of the circuit diagram and how to connect it both physically and within Simulink:

- Circuit Diagram: Visual representation of the circuits in Position 1 and Position 2 with component connections.
- Simulink Implementation: Step-by-step instructions to build, configure, and simulate the circuit in Simulink.
- Understanding the Results: Guidance on what to expect from the simulation and how to interpret the results.

By following these instructions, you should be able to:

- Construct the circuit with the correct connections and components.
- Implement the switching mechanism using the Step block and Ideal Switch.
- Simulate the circuit's behavior over time and compare it with the analytical solution.
- Analyze the inductor current waveform to understand the circuit's transient and steady-state responses.

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Feel free to ask if you need further assistance with any step or if you have additional questions about the circuit or the simulation process.

ekanshkhullar9 wrote:

does resistor other end connect to the switch ryt

Answer:

Yes, you're absolutely correct—the other end of each resistor connects to the switch. This configuration is essential to control which circuit (Position 1 or Position 2) is connected to the inductor at any given time in your Simulink model. By connecting the resistors to the switch, you ensure that the switching action at $ t = 0 $ correctly simulates the transition between the two circuit configurations.

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Detailed Step-by-Step Explanation

1. Understanding the Circuit Configuration

Position 1 (Before $ t = 0 $):

- Components:
- Voltage Source: 20 V DC
- Resistor: 5 Ω
- Inductor: 0.5 H

- Connections:
1. 20 V Voltage Source:
- Positive Terminal connects to one end of the 5 Ω resistor.
- Negative Terminal connects to ground.
2. 5 Ω Resistor:
- One End: Connected to the positive terminal of the 20 V source.
- Other End: Connected to Switch Terminal 1.
3. Switch Terminal 1:
- Connects to the common terminal of the switch when in Position 1.
4. Common Terminal of the Switch:
- Connected to one end of the inductor (0.5 H).
5. Inductor:
- Other End connects to ground.

Position 2 (After $ t = 0 $):

- Components:
- Voltage Source: 40 V DC
- Resistor: 2 Ω
- Inductor: 0.5 H (same as in Position 1)

- Connections:
1. 40 V Voltage Source:
- Positive Terminal connects to one end of the 2 Ω resistor.
- Negative Terminal connects to ground.
2. 2 Ω Resistor:
- One End: Connected to the positive terminal of the 40 V source.
- Other End: Connected to Switch Terminal 2.
3. Switch Terminal 2:
- Connects to the common terminal of the switch when in Position 2.
4. Common Terminal of the Switch:
- Connected to one end of the inductor (0.5 H).
5. Inductor:
- Other End connects to ground.

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2. Role of the Switch in the Circuit

- Switch Functionality:
- The switch determines which voltage source and resistor are connected to the inductor.
- Before $ t = 0 $: The switch connects Terminal 1 (Position 1) to the common terminal.
- After $ t = 0 $: The switch connects Terminal 2 (Position 2) to the common terminal.

- Connection to Resistors:
- The other end (the end not connected to the voltage source) of each resistor connects to its respective switch terminal.
- 5 Ω Resistor: Connects to Switch Terminal 1.
- 2 Ω Resistor: Connects to Switch Terminal 2.

- Inductor Connection:
- The common terminal of the switch is connected to the inductor.
- This ensures that the inductor is part of the active circuit path determined by the switch position.

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Supporting Details and Explanations

A. Implementing the Circuit in Simulink

1. Adding Components:
- Voltage Sources: Use two DC Voltage Source blocks set to 20 V and 40 V.
- Resistors: Use Resistor blocks set to 5 Ω and 2 Ω.
- Inductor: Use an Inductor block set to 0.5 H.
- Ideal Switch: Use an Ideal Switch block to represent the switching action.
- Step Block: Use a Step block to control the switch timing at $ t = 0 $.
- Grounds: Ensure all grounds are properly connected using Ground blocks.

2. Connecting Components:
- Position 1 Circuit:
- Connect the positive terminal of the 20 V source to one end of the 5 Ω resistor.
- Connect the other end of the 5 Ω resistor to Switch Terminal 1.
- The negative terminal of the 20 V source connects to ground.
- Position 2 Circuit:
- Connect the positive terminal of the 40 V source to one end of the 2 Ω resistor.
- Connect the other end of the 2 Ω resistor to Switch Terminal 2.
- The negative terminal of the 40 V source connects to ground.
- Switch Common Terminal:
- Connect the common terminal of the switch to one end of the inductor (0.5 H).
- Inductor:
- Connect the other end of the inductor to ground.
- Switch Control:
- Connect the Step block output to the control input of the Ideal Switch.

3. Configuring the Step Block:
- Step Time: Set to `0` (switching occurs at $ t = 0 $).
- Initial Value: `0` (switch is in Position 1 before $ t = 0 $).
- Final Value: `1` (switch moves to Position 2 after $ t = 0 $).

4. Setting Initial Conditions:
- Inductor Initial Current: Set to `4 A` to represent the steady-state current before switching (calculated from Position 1).

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B. Simulation Flow

- Before $ t = 0 $:
- Switch State: The switch connects Terminal 1 to the common terminal.
- Active Circuit Path: 20 V source → 5 Ω resistor → Inductor → Ground.
- Circuit Behavior: The inductor carries a steady-state current of `4 A`.

- At $ t = 0 $:
- Switch Action: The Step block output changes from `0` to `1`, triggering the switch.
- Switch State: The switch connects Terminal 2 to the common terminal.

- After $ t = 0 $:
- Active Circuit Path: 40 V source → 2 Ω resistor → Inductor → Ground.
- Circuit Behavior: The current through the inductor changes according to the circuit's transient response.

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Caveats and Additional Considerations

1. Ensuring Correct Switch Configuration:
- Verify that the Ideal Switch block is correctly set up to switch between Terminal 1 and Terminal 2 based on the control signal.
- Check the switch parameters, such as Threshold Voltage, to ensure it responds accurately to the Step block output.

2. Solver Settings:
- Use a suitable solver for simulating switching events.
- Recommended Solver: `ode23tb` (stiff/TR-BDF2) for handling stiff systems.
- Set the simulation start and stop times appropriately (e.g., `0` to `5` seconds).

3. Ground Connections:
- Ensure that all voltage sources' negative terminals and the inductor's other end are connected to ground for a complete circuit.

4. Initial Conditions Consistency:
- The inductor's initial current must match the calculated steady-state current from Position 1 to avoid simulation inaccuracies.

5. Validation of Results:
- After running the simulation, compare the inductor current waveform with the analytical expression:
$$ I(t) = -16 e^{-4t} + 20 \, \text{A}, \quad t \geq 0 $$
- Ensure that the simulation results align with theoretical expectations.

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Summary

To summarize:

- Yes, the other end of each resistor connects to the switch in your circuit.
- This connection allows the switch to control which voltage source and resistor are connected to the inductor at any given time.
- By setting up the circuit in this manner, you can accurately simulate the switching action at $ t = 0 $ and observe the transient behavior of the inductor current.
- Ensure all components are correctly connected and configured in your Simulink model to reflect the physical circuit accurately.

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Feel free to ask if you need further clarification or assistance with setting up your Simulink model or understanding the circuit connections. I'm here to help you succeed in your simulation and analysis.