Ohm's Law and Electrical Circuits: Series and Parallel
Why Ohm's Law Is the Foundation of Every Electrical Circuit
Imagine standing in front of an industrial control panel packed with breakers, resistors, and wires, and one motor refuses to start. Where do you begin troubleshooting? The answer always starts with Ohm's Law — the equation that links voltage, current, and resistance in every electrical circuit on Earth.
In this lesson we dive deep into Ohm's Law, explore series and parallel circuits, learn Kirchhoff's laws, and finish with practical applications you encounter daily in factory panels.
Ohm's Law: The Golden Relationship
In 1827, German physicist Georg Simon Ohm discovered that the current flowing through a conductor is directly proportional to the applied voltage and inversely proportional to its resistance:
V = I × R
Where:
- V = voltage in volts (V)
- I = current in amperes (A)
- R = resistance in ohms (Ω)
Rearranging for any unknown:
- Current:
I = V / R - Resistance:
R = V / I
Industrial Example
A heating element in an industrial oven has a resistance of 48Ω connected to a 220V supply. What current flows through it?
I = V / R = 220 / 48 = 4.58A
Power consumed:
P = V × I = 220 × 4.58 = 1007W ≈ 1kW
This simple calculation determines the wire gauge and circuit breaker rating you select.
Series Circuits: The Single Path
In a series circuit, components are connected end-to-end along a single path. The same current flows through every element.
Series Circuit Properties
| Property | Rule |
|---|---|
| Current | Same through all elements: I = I₁ = I₂ = I₃ |
| Voltage | Splits across elements: V = V₁ + V₂ + V₃ |
| Total resistance | Sum of all resistances: R_total = R₁ + R₂ + R₃ |
Worked Example
Three resistors — 10Ω, 20Ω, and 30Ω — are connected in series across a 120V source:
R_total = 10 + 20 + 30 = 60Ω
I = 120 / 60 = 2A (same through all resistors)
V₁ = 2 × 10 = 20V
V₂ = 2 × 20 = 40V
V₃ = 2 × 30 = 60V
Notice the voltage drops sum to 20 + 40 + 60 = 120V — exactly the source voltage.
The Drawback in Industry
If any element in a series circuit fails open, the entire circuit loses power — like old-fashioned Christmas lights where one burnt bulb kills the whole string. This is why critical industrial loads are never wired in series.
Parallel Circuits: The Industrial Choice
In a parallel circuit, all components share the same two connection nodes. Every branch sees the full source voltage.
Parallel Circuit Properties
| Property | Rule |
|---|---|
| Voltage | Same across all branches: V = V₁ = V₂ = V₃ |
| Current | Splits among branches: I = I₁ + I₂ + I₃ |
| Total resistance | 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ |
Worked Example
Three loads in a distribution panel — 60Ω, 120Ω, and 40Ω — connected in parallel across 220V:
1/R_total = 1/60 + 1/120 + 1/40 = 0.0167 + 0.0083 + 0.025 = 0.05
R_total = 1/0.05 = 20Ω
I_total = 220 / 20 = 11A
I₁ = 220 / 60 = 3.67A
I₂ = 220 / 120 = 1.83A
I₃ = 220 / 40 = 5.5A
The total parallel resistance is always less than the smallest individual resistance — because each branch opens an additional path for current.
Why Factories Use Parallel Wiring
- Every device gets the full supply voltage (
220Vor380V) - One device failing does not stop the others
- New loads can be added without affecting existing equipment
Mixed Circuits: The Industrial Reality
Most real-world industrial circuits combine series and parallel elements. For example: a 2Ω protection resistor in series with a bank of parallel-connected lamps.
To solve these: first reduce the parallel group to a single equivalent resistance, then add it to the series resistance.
Kirchhoff's Laws: The Advanced Toolkit
When circuits grow complex — multiple loops and different voltage sources — Ohm's Law alone is not enough. That is where Kirchhoff's laws come in, formulated by German physicist Gustav Kirchhoff in 1845.
First Law: Kirchhoff's Current Law (KCL)
The sum of currents entering any node equals the sum of currents leaving it.
ΣI_in = ΣI_out
Consider a junction in a distribution panel receiving 20A. If two branches draw 8A and 5A, the third branch draws:
I₃ = 20 - 8 - 5 = 7A
KCL is simply conservation of charge — electrons neither vanish nor appear from nothing.
Second Law: Kirchhoff's Voltage Law (KVL)
The sum of all voltages around any closed loop equals zero.
ΣV = 0
Consider a loop with a 12V battery and two resistors R₁ = 4Ω and R₂ = 2Ω:
12 - I×4 - I×2 = 0
12 = 6I
I = 2A
KVL means every joule the source provides is fully consumed by the resistors — energy is neither lost nor created.
Voltage Dividers: The Practical Workhorse
A voltage divider is a simple two-resistor series circuit used to obtain a lower voltage from a higher source without a transformer.
V_out = V_in × (R₂ / (R₁ + R₂))
Example: Scaling a 24V Source to 10V for a Sensor Signal
You need 10V from a 24V supply:
V_out / V_in = R₂ / (R₁ + R₂) = 10/24 = 0.417
Choosing R₂ = 10kΩ:
R₁ = R₂ × (V_in/V_out - 1) = 10k × (24/10 - 1) = 10k × 1.4 = 14kΩ
Industrial Applications of Voltage Dividers
- Scaling sensor signals to PLC-compatible levels
- Setting reference points in analog control circuits
- Monitoring battery levels in UPS systems
- Generating reference voltages for comparators
Practical Applications in Industrial Control Panels
Wire Sizing
In an industrial panel, a 5kW single-phase motor running at 380V:
I = P / V = 5000 / 380 = 13.16A
From wire tables: a 2.5mm² copper conductor handles up to 21A — suitable with a safety margin.
Circuit Breaker Selection
The breaker rating must exceed normal operating current but stay below the wire's capacity:
I_operating < I_breaker < I_wire
13.16A < 16A < 21A
Voltage Drop in Cables
In a factory, a 4mm² copper cable runs 50m to a 15A load:
Copper resistivity ≈ 0.0175 Ω·mm²/m
R = ρ × L / A = 0.0175 × (2 × 50) / 4 = 0.4375Ω
Voltage drop = I × R = 15 × 0.4375 = 6.56V
As a percentage: 6.56 / 220 × 100 = 2.98%
Industrial standards typically allow 3% to 5% maximum voltage drop — we are right at the limit.
Comparison Table: Series vs Parallel
| Criterion | Series | Parallel |
|---|---|---|
| Current | Same through all elements | Splits by resistance |
| Voltage | Splits across elements | Same across all branches |
| Total resistance | Greater than largest R | Less than smallest R |
| Effect of one failure | Entire circuit stops | Other branches continue |
| Industrial use | Protection resistors, voltage dividers | Load distribution, panels |
| Adding loads | Reduces total current | Increases total current |
Key Formulas Summary
| Law | Formula | When to Use |
|---|---|---|
| Ohm's Law | V = I × R |
Any simple circuit |
| KCL (Kirchhoff's Current) | ΣI = 0 at a node |
Multi-branch circuits |
| KVL (Kirchhoff's Voltage) | ΣV = 0 in a loop |
Multi-loop circuits |
| Voltage divider | V_out = V_in × R₂/(R₁+R₂) |
Obtaining a partial voltage |
| Power | P = V × I = I²R = V²/R |
Calculating consumption and heating |
Summary
Ohm's Law and Kirchhoff's laws are not theoretical equations that stay in textbooks — they are the tools every electrical engineer uses daily to design circuits, size breakers, and diagnose faults. Practice calculating current, voltage, and resistance in series and parallel circuits, and you will find that troubleshooting any distribution panel becomes systematic instead of random. Remember: the voltage divider is the simplest and most widespread circuit in industrial control — master it and you will understand how sensors communicate with controllers.