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

Find the current:

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

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

series resistors, total resistance, ohm's law, voltage drop, current flow, resistors in series, electrical circuit, circuit analysis, resistance calculation, voltage division, current calculation, resistor network, Python circuit simulation, series circuit, voltage across resistors, total voltage, resistive circuit, circuit formula, electric current, electronics basics, nerd cafe

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Last updated 1 month ago

# 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")

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)