In engineering, **difference equations** allow you to model how systems evolve step by step over time. This method is especially useful when you want to simulate physical processes that change continuously, such as the charging of a capacitor in an `RC` (resistor-capacitor) circuit. By updating the state of the system in small increments, you can approximate its behavior and visualize how variables like voltage change in response to inputs and system parameters. This approach is a cornerstone in the simulation of real-world engineering systems.


import unittest
import user_code
import ast
import re   
import importlib
import csv
import unittest
import importlib

class TestTask(unittest.TestCase):
    def test_return_types_and_lengths(self):
        import user_code
        importlib.reload(user_code)
        V_source = 5.0
        R = 1000
        C = 0.001
        V0 = 0.0
        dt = 0.01
        total_time = 1.0
        times, voltages = user_code.simulate_rc_circuit(V_source, R, C, V0, dt, total_time)
        _dynamic_test(
            self,
            isinstance(times, list) and isinstance(voltages, list),
            "Function returns lists for times and voltages.",
            f"Expected lists, got {type(times)} and {type(voltages)}."
        )
        _dynamic_test(
            self,
            len(times) == len(voltages),
            "Times and voltages lists have equal length.",
            f"Length mismatch: times={len(times)}, voltages={len(voltages)}."
        )

    def test_initial_voltage(self):
        import user_code
        importlib.reload(user_code)
        V_source = 5.0
        R = 1000
        C = 0.001
        V0 = 0.0
        dt = 0.01
        total_time = 1.0
        times, voltages = user_code.simulate_rc_circuit(V_source, R, C, V0, dt, total_time)
        _dynamic_test(
            self,
            len(voltages) > 0 and abs(voltages[0] - V0) < 1e-8,
            "Initial voltage equals V0.",
            f"Initial voltage: {voltages[0]}, expected: {V0}."
        )

    def test_final_voltage_below_source(self):
        import user_code
        importlib.reload(user_code)
        V_source = 5.0
        R = 1000
        C = 0.001
        V0 = 0.0
        dt = 0.01
        total_time = 1.0
        times, voltages = user_code.simulate_rc_circuit(V_source, R, C, V0, dt, total_time)
        _dynamic_test(
            self,
            len(voltages) > 0 and voltages[-1] <= V_source + 1e-8,
            "Final voltage is less than or equal to source voltage.",
            f"Final voltage: {voltages[-1]}, source: {V_source}."
        )

    def test_time_list_start_end(self):
        import user_code
        importlib.reload(user_code)
        V_source = 5.0
        R = 1000
        C = 0.001
        V0 = 0.0
        dt = 0.01
        total_time = 1.0
        times, voltages = user_code.simulate_rc_circuit(V_source, R, C, V0, dt, total_time)
        _dynamic_test(
            self,
            len(times) > 0 and abs(times[0] - 0.0) < 1e-8,
            "Time list starts at 0.",
            f"Start of time list: {times[0]}, expected: 0.0."
        )
        _dynamic_test(
            self,
            len(times) > 0 and abs(times[-1] - total_time) < 1e-8,
            "Time list ends at total_time.",
            f"End of time list: {times[-1]}, expected: {total_time}."
        )

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

def normalize_text(text):
    text = text.lower()
    text = re.sub(r"\\s{2,}", " ", text)
    text = re.sub(r"\\s*([,:?])\\s*", r"\\1 ", text)
    return text.strip()

def change_var(code: str, var_name: str, value: str) -> str:
    tree = ast.parse(code)
    lines = code.splitlines()
    changed = False
    # Collect all assignment nodes to modify
    assign_nodes = [
        (i, node)
        for i, node in enumerate(tree.body)
        if isinstance(node, ast.Assign)
        and any(isinstance(target, ast.Name) and target.id == var_name for target in node.targets)
    ]

    # If nothing to change, return unmodified code
    if not assign_nodes:
        return code

    # Perform replacements for all matching assignments (from last to first to not break line offsets)
    for i, node in reversed(assign_nodes):
        start_line = node.lineno - 1
        line = lines[start_line]
        indent = ' ' * (len(line) - len(line.lstrip()))
        lines[start_line] = f"{indent}{var_name} = {value}"
        next_line = len(lines)
        for next_node in tree.body[i+1:]:
            if hasattr(next_node, 'lineno'):
                next_line = next_node.lineno - 1
                break
        if next_line > start_line + 1:
            lines[start_line+1:next_line] = []
        changed = True

    return '\\n'.join(lines) if changed else code

if __name__ == "__main__":
    unittest.main()


test_main.py

A practical course designed for engineers who want to leverage Python to solve real-world engineering problems. Explore data analysis, mathematical modeling, and simulation using Python's powerful libraries and tools, all through engaging, hands-on examples and challenges.

Learn how to use Python to analyze, summarize, and visualize engineering data. This section covers essential data handling and visualization techniques tailored for engineering applications.

Dive into mathematical modeling and simulation techniques for engineering systems using Python. Learn to model physical processes, solve equations, and simulate system behavior.

Apply data science techniques to engineering problems, including classification, clustering, and predictive modeling using Python's scikit-learn and seaborn libraries.

Challenge: Simulate RC Circuit Charging

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