Parallel Resistors

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In parallel circuits, resistors are connected such that they share both terminals. In this configuration, the voltage across each resistor is the same, but currents can vary.

Mathematical Formula:

If you have n resistors connected in parallel:

$$\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+...+\frac{1}{R_{n}}$$

Where:

• R_Req​: equivalent or total resistance

• R₁,R₂,…,R_n​: individual resistances

For 2 resistors only:

$$R_{eq}=\frac{R_{1}.R_{2}}{R_{1}+R_{2}}$$

Numerical Example:

Let’s calculate the equivalent resistance of these resistors in parallel:

• R₁=10Ω

• R₂​=20Ω

• R₃=30Ω

Using the formula:

$$\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{20}+\frac{1}{30}=0.1+0.05+0.0333=0.1833\Rightarrow R_{eq}=\frac{1}{0.1833}≈5.45Ω$$

Python Code: Step-by-Step Parallel Resistance Calculator

def calculate_parallel_resistance():
    # Step 1: Ask user how many resistors are in parallel
    num = int(input("Enter the number of resistors in parallel: "))

    # Step 2: Initialize list to store resistors
    resistors = []

    # Step 3: Input resistor values
    for i in range(num):
        value = float(input(f"Enter value of resistor R{i+1} (in ohms): "))
        resistors.append(value)

    # Step 4: Calculate equivalent resistance using reciprocal sum
    reciprocal_sum = 0
    for R in resistors:
        reciprocal_sum += 1 / R

    if reciprocal_sum == 0:
        print("Error: Division by zero!")
        return

    Req = 1 / reciprocal_sum

    # Step 5: Show results
    print(f"\nResistor values: {resistors}")
    print(f"Equivalent parallel resistance: {Req:.4f} ohms")

# Run the function
calculate_parallel_resistance()

Output:

Enter the number of resistors in parallel:  3
Enter value of resistor R1 (in ohms):  10
Enter value of resistor R2 (in ohms):  20
Enter value of resistor R3 (in ohms):  30

Resistor values: [10.0, 20.0, 30.0]
Equivalent parallel resistance: 5.4545 ohms

Keywords

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