Resistance in Series and Parallel Circuits
Electronic circuits often contain several resistors connected together. Depending on whether the resistors are connected in series or in parallel, the total or equivalent resistance of the circuit changes significantly.
Series Connection
In a series circuit, resistors are connected one after another so there is only one path for current to flow.
The same current flows through every resistor, while the voltage is divided between them.
The total resistance is simply the sum of all the individual resistances.
Example: Series Resistors
Three resistors are connected in series:
- R₁ = 100 Ω
- R₂ = 220 Ω
- R₃ = 680 Ω
Total resistance:
100 Ω + 220 Ω + 680 Ω = 1000 Ω (1 kΩ)
Adding more resistors in series always increases the total resistance.
Characteristics of Series Circuits
- Only one path for current.
- The same current flows through every resistor.
- Voltage is divided across the resistors.
- Total resistance is greater than any individual resistor.
Parallel Connection
In a parallel circuit, all resistors are connected across the same two points.
Each resistor has the same voltage across it, while the current divides between the branches.
Adding more resistors in parallel always reduces the equivalent resistance.
Example: Parallel Resistors
Two equal resistors are connected in parallel:
- R₁ = 100 Ω
- R₂ = 100 Ω
Equivalent resistance:
R = 50 Ω
The total resistance is lower than either resistor alone because current has two separate paths through the circuit.
Series vs Parallel Resistance
| Series | Parallel |
|---|---|
| One current path. | Multiple current paths. |
| Current is the same everywhere. | Current divides between branches. |
| Voltage divides. | Voltage is the same across every branch. |
| Total resistance increases. | Total resistance decreases. |
Practical Applications
| Application | Connection Type |
|---|---|
| Voltage divider | Series |
| LED current limiting | Series |
| Power resistor banks | Parallel |
| Speaker crossover networks | Series and Parallel |
| Current sharing circuits | Parallel |
| Load balancing | Parallel |
Why Parallel Resistance is Lower
When resistors are connected in parallel, the electric current has multiple paths to follow.
The additional paths make it easier for current to flow, reducing the overall opposition to current.
This is similar to opening additional lanes on a busy highway—traffic flows more easily because there are more routes available.
Common Mistakes
- Adding parallel resistors directly as if they were in series.
- Confusing voltage division with current division.
- Assuming equal current flows in parallel branches.
- Ignoring the effect of resistor tolerance.
Key Points
- Series resistances add together.
- Parallel resistances always produce a lower equivalent resistance.
- Series circuits have one current path.
- Parallel circuits have multiple current paths.
- Voltage divides in series circuits.
- Current divides in parallel circuits.
- Equivalent resistance simplifies circuit analysis.