Series Resistors

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1. What Are Series Resistors?

When resistors are connected end-to-end (in a single path), they are said to be connected in series.

Key Characteristics:

• Same Current flows through all resistors.

• Voltage is divided across the resistors.

• Total resistance is the sum of all individual resistances.

2. Formula for Series Resistors

Let’s say we have n resistors:

$$R_{1},R_{2},R_{3},...,R_{n}$$

Total Resistance:

$$R_{Total}=R_{1}+R_{2}+R_{3}+...+R_{n}$$

Current in Circuit (Ohm's Law):

$$I=\frac{V}{R_{Total}}$$

Voltage Across Each Resistor:

$$V_{i}=R_{i}\times I$$

3. Example Problem (Manual Calculation)

Example 1:

You have 3 resistors in series:

• R1=10 Ω

• R2=20 Ω

• R3=30 Ω

And the total voltage supplied is 𝑉 = 60 V .

1. Find total resistance:

$$R_{total}=10+20+30=60Ω$$

1. Find the current:

$$I=\frac{V}{R_{Total}}=\frac{60}{60}=1\;\;(A)$$

1. Voltage across each resistor:

$$V_{1}=10\times 1=10 \;\;V_{2}=20\times 1=20\;\;V_{3}=30\times 1=30$$

4. Python Code Example

Let’s now simulate this using Python.

Python Code:

# Series resistor circuit calculator

# Given resistor values in ohms
resistors = [10, 20, 30]
# Total voltage supplied (Volts)
V_total = 60

# Calculate total resistance
R_total = sum(resistors)

# Calculate current using Ohm's law
I = V_total / R_total

# Calculate voltage across each resistor
voltages = [I * R for R in resistors]

# Display results
print(f"Resistor values: {resistors} ohms")
print(f"Total Resistance: {R_total} ohms")
print(f"Total Current: {I:.2f} A")
print("Voltages across each resistor:")
for idx, V in enumerate(voltages, start=1):
    print(f"  V{idx} = {V:.2f} V")

Output

Resistor values: [10, 20, 30] ohms
Total Resistance: 60 ohms
Total Current: 1.00 A
Voltages across each resistor:
  V1 = 10.00 V
  V2 = 20.00 V
  V3 = 30.00 V

5. Visualization (Optional)

Let’s plot the voltage drop:

import matplotlib.pyplot as plt

def plot_voltage_drops(resistors, V_total):
    R_total = sum(resistors)
    I = V_total / R_total
    voltages = [I * R for R in resistors]

    plt.figure(figsize=(8, 4))
    plt.bar([f'R{i+1}' for i in range(len(resistors))], voltages, color='skyblue')
    plt.title('Voltage Drop Across Series Resistors')
    plt.ylabel('Voltage (V)')
    plt.grid(True, axis='y')
    plt.show()

# Example
plot_voltage_drops([10, 20, 30], 60)

Output

Keywords

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