Lære Series and Parallel Circuits | Circuit Analysis with Python

Understanding how resistors combine in series and parallel is fundamental to circuit design and analysis. In a series configuration, resistors are connected end-to-end so that the same current flows through each resistor. The total resistance in this arrangement is simply the sum of the individual resistances. This is important when you want to increase resistance in a circuit or control current flow precisely. In contrast, a parallel configuration connects all resistor terminals together at each end, creating multiple paths for current. Here, the voltage across each resistor is the same, but the total resistance decreases as more resistors are added. Parallel circuits are commonly used to distribute current or reduce overall resistance without changing the voltage.


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def total_resistance_series(resistances):
    """
    Calculate total resistance for resistors in series.
    Args:
        resistances (list of float): List of resistor values in ohms.
    Returns:
        float: Total resistance in ohms.
    """
    return sum(resistances)

def total_resistance_parallel(resistances):
    """
    Calculate total resistance for resistors in parallel.
    Args:
        resistances (list of float): List of resistor values in ohms.
    Returns:
        float: Total resistance in ohms.
    """
    if not resistances or 0 in resistances:
        return 0.0
    reciprocal_sum = sum(1.0 / r for r in resistances)
    return 1.0 / reciprocal_sum if reciprocal_sum != 0 else 0.0

You can use these Python functions to analyze more complex resistor networks by breaking them down into combinations of series and parallel groups. For example, in a circuit with both series and parallel sections, first calculate the equivalent resistance of each parallel or series subset, then combine these results step by step. This approach allows you to solve for the total resistance of nearly any resistor network, which is essential for predicting current, voltage, and power distribution in practical electrical systems.


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# Example: Calculate total resistance for a circuit where
# R1 and R2 are in parallel, and their combination is in series with R3.

R1 = 100  # ohms
R2 = 200  # ohms
R3 = 50   # ohms

# First, find the equivalent resistance of R1 and R2 in parallel.
parallel_eq = total_resistance_parallel([R1, R2])

# Then, add R3 in series.
total_eq = total_resistance_series([parallel_eq, R3])

print(f"Equivalent resistance of the circuit: {total_eq:.2f} ohms")

1. How does total resistance change when resistors are added in series?

2. What is the formula for combining two resistors in parallel?

3. In which configuration does the total resistance always decrease when adding more resistors?

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Suggested prompts:

Can you explain how the total resistance was calculated in the example?

What happens if one of the resistors has a value of zero?

Can you show how to analyze a more complex resistor network?

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