Resistors in Series and Parallel

Introduction

Resistors are the simplest yet most powerful tools in electronics. They control current, divide voltage, and protect sensitive components. But resistors rarely work alone. In real circuits, they are combined in different ways to achieve desired resistance values. The two most common combinations are series and parallel connections.

Understanding how resistors behave in these configurations is essential for every student. It helps in designing circuits, troubleshooting, and predicting performance. In this blog, we’ll explore resistors in series and parallel, derive formulas, and work through practical examples.

 

Resistors in Series

Definition

Resistors are said to be in series when they are connected end‑to‑end, so the same current flows through each resistor.

 

Formula

The total resistance in series is simply the sum of individual resistances:

Rtotal = R1 + R2 + R3 +…

 

Why?

Because current is the same through all resistors, but voltage drops add up. Each resistor consumes part of the total voltage.

Example

Suppose three resistors are connected in series:

• R1=100 Ω
• R2=200 Ω
• R3=300 Ω

Rtotal = 100 + 200 + 300 = 600 Ω

If a 12V battery is connected, the current is:

I = V / Rtotal =12 / 600=0.02 A (20 mA)

Voltage drops across each resistor:

• V1 = I x R1 = 0.02 x 100 = 2 V
• V2 = 0.02 x 200 = 4 V
• V3 = 0.02 x 300 = 6 V

Notice how the voltages add up to 12V.

Applications

• Voltage division (voltage divider circuits).
• Current limiting in series LED strings.
• Creating precise resistance values by combining standard resistors.

 

Resistors in Parallel

Definition

Resistors are in parallel when both ends of each resistor are connected together. This means the voltage across each resistor is the same, but the current divides among them.

Formula

The reciprocal of total resistance is the sum of reciprocals:

1 / Rtotal = 1/R1 + 1/R2 + 1/R3+…

 

For Two Resistors:

Rtotal=R1⋅R2 / (R1+R2)

 

Why?

Because each resistor provides an independent path for current. More paths mean lower overall resistance.

Example

Suppose two resistors are connected in parallel:

• R1=100 Ω
• R2=200 Ω

1 / Rtotal = (1 / 100) + (1 / 200) = 0.01 + 0.005 = 0.015

Rtotal=1 / 0.015 ≈ 66.7 Ω

 

If a 12V battery is connected, the current is:

I = V / Rtotal = 12 / 66.7 ≈ 0.18 A

 

Current through each resistor:

• I1 = 12 / 100 = 0.12 A
• I2  = 12 / 200 = 0.06 A

Total current = 0.12 + 0.06 = 0.18 A (matches calculation).

 

Applications

• Reducing resistance values.
• Increasing current capacity (parallel resistors share load).
• Ensuring redundancy in circuits.

 

Series vs. Parallel: Key Differences

Feature	Series	Parallel
Current	Same through all resistors	Divides among resistors
Voltage	Divides across resistors	Same across all resistors
Total Resistance	Larger than any individual resistor	Smaller than the smallest resistor
Applications	Voltage division, biasing	Current sharing, lowering resistance

 

Mixed Combinations

Real circuits often use a mix of series and parallel.

Example: Three resistors:

• R1 = 100 Ω
• R2 = 200 Ω
• R3 = 300 Ω

Suppose R2 and R3 are in parallel, and that combination is in series with R1.

Step 1: Parallel of R2 and R3:

R23 = 200⋅300 / (200+300) = 60000 / 500 = 120 Ω

 

Step 2: Add series R1:

Rtotal = R1 + R23 = 100 + 120 = 220 Ω

This shows how series and parallel can be combined to achieve desired resistance.

 

Practical Experiments for Students

1. Series Circuit: Connect three resistors in series with a battery. Measure voltage across each resistor with a multimeter. Verify that voltages add up to supply voltage.
2. Parallel Circuit: Connect two resistors in parallel. Measure current through each branch. Verify that total current equals sum of branch currents.
3. Mixed Circuit: Build a series‑parallel combination. Calculate expected resistance, then measure with a multimeter. Compare theory and practice.

These experiments help students see the math come alive in real circuits.

 

Real‑World Applications

• LED Arrays: Series resistors limit current, parallel resistors balance brightness.
• Power Supplies: Parallel resistors share load to prevent overheating.
• Voltage Dividers: Series resistors create reference voltages for sensors.
• Current Shunts: Parallel resistors measure current in industrial systems.
• Safety: Parallel resistors provide redundancy in critical circuits.

 

Common Mistakes Students Make

• Forgetting that series increases resistance while parallel decreases resistance.
• Misapplying Ohm’s Law (using wrong voltage or current values).
• Ignoring tolerance and power rating.
• Not checking units (Ω, mA, V).

 

Key Takeaways

• Series: resistances add, current same, voltage divides.
• Parallel: reciprocals add, voltage same, current divides.
• Mixed circuits combine both rules.
• Always verify with Ohm’s Law and a multimeter.
• Applications range from simple LED circuits to industrial automation.

 

Closing Remarks

Resistors in series and parallel are the building blocks of circuit design. By mastering these configurations, students gain confidence in analysing and building circuits. Whether it’s a classroom experiment or a real‑world project, the principles remain the same: series adds resistance, parallel reduces it, and together they shape the flow of electricity.