Resistors in Parallel
When two or more resistors are connected across the same two points, they are said to be connected in parallel. In a parallel circuit, every resistor has the same voltage across it, while the total current is shared between the different branches. Parallel resistor networks are widely used in power supplies, current sharing, voltage sensing, electronic loads, and many other electronic circuits.
What Is a Parallel Connection?
A parallel connection joins all resistor terminals to the same two electrical nodes.
This means every resistor experiences exactly the same voltage, while the current divides between the available paths according to the resistance of each branch.
Characteristics of Parallel Circuits
- All resistors share the same voltage.
- The current divides between the branches.
- The total current equals the sum of the branch currents.
- The equivalent resistance is always lower than the smallest resistor.
- If one branch becomes open circuit, the remaining branches continue to operate.
Equivalent Resistance
The equivalent resistance of resistors connected in parallel is calculated using the reciprocal formula below.
For only two resistors, a convenient shortcut is:
RT = (R1 × R2) ÷ (R1 + R2)
Example 1 – Two Equal Resistors
Two 100 Ω resistors are connected in parallel.
RT = (100 × 100) ÷ (100 + 100) RT = 10000 ÷ 200 RT = 50 Ω
Two identical resistors connected in parallel always produce a resistance equal to half the value of one resistor.
Example 2 – Different Resistor Values
Three resistors are connected in parallel:
- 100 Ω
- 220 Ω
- 470 Ω
1/RT = 1/100 + 1/220 + 1/470 RT ≈ 62.3 Ω
Current Distribution
The current flowing through each resistor is determined by Ohm's Law.
I = V ÷ R
Lower resistance branches carry more current, while higher resistance branches carry less.
Worked Example
A 12 V supply is connected across two resistors:
- 100 Ω
- 300 Ω
| Resistor | Current |
|---|---|
| 100 Ω | 120 mA |
| 300 Ω | 40 mA |
| Total | 160 mA |
Power Dissipation
The power dissipated by each resistor depends on the voltage across it and its resistance.
P = V² ÷ R
Since every branch has the same voltage, lower-value resistors dissipate more power because they carry more current.
Practical Applications
- Current sharing circuits.
- Power resistor banks.
- LED arrays.
- Current sensing.
- Electronic loads.
- Audio crossover networks.
- Power supply filters.
- Battery management systems.
Advantages
- All branches receive the full supply voltage.
- One failed branch usually does not stop the others from working.
- Current is shared between resistors.
- Equivalent resistance can be reduced easily.
- Useful for increasing power-handling capability.
Disadvantages
- Current calculations are more complex than in series circuits.
- Lower equivalent resistance increases total current demand.
- Power supply must be capable of supplying the increased current.
Common Mistakes
| Mistake | Explanation |
|---|---|
| Adding resistor values together. | Only series resistors are added directly. |
| Assuming current is identical in every branch. | Current depends on each branch resistance. |
| Ignoring power ratings. | Each resistor dissipates its own power. |
| Believing the equivalent resistance is larger than the smallest resistor. | The equivalent resistance is always lower than the smallest branch resistance. |
Real-World Examples
| Application | Purpose |
|---|---|
| Power Amplifiers | Emitter resistors sharing current. |
| Electronic Dummy Loads | Increasing power dissipation. |
| High-Power LED Arrays | Current distribution. |
| Bench Power Supplies | Parallel shunt resistors for current measurement. |
| Battery Packs | Voltage monitoring networks. |
Key Points
- Parallel resistors share the same voltage.
- The total current equals the sum of all branch currents.
- Current divides according to resistance.
- The equivalent resistance is always less than the smallest resistor.
- Parallel circuits are widely used in practical electronic design.