What Are Resistors in Parallel?

Resistors are connected in parallel when both ends of each resistor are connected to the same two electrical nodes.

              ┌───/\/\/\─── R1 ───┐
              │                   │
+V ───────────┼───/\/\/\─── R2 ───┼──────── GND
              │                   │
              └───/\/\/\─── R3 ───┘

Unlike a series circuit, the voltage across every parallel resistor is the same.

Equivalent Resistance

For two or more resistors connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

1
── = 1/R1 + 1/R2 + 1/R3 + ...
RT

For two resistors, the formula can be simplified to:

RT = (R1 × R2) / (R1 + R2)

Parallel Resistor Calculator

Example — Two Resistors in Parallel

Suppose a 100 Ω resistor and a 220 Ω resistor are connected in parallel.

R1 = 100 Ω

R2 = 220 Ω

The equivalent resistance is:

RT = (100 × 220) / (100 + 220)

RT = 22000 / 320

RT = 68.75 Ω

Therefore, the equivalent resistance is 68.75 Ω.

Important Rule for Parallel Resistors

The equivalent resistance of parallel resistors is always lower than the smallest individual resistor.

For example, if 100 Ω and 220 Ω are connected in parallel:

Smallest resistor = 100 Ω

Equivalent resistance = 68.75 Ω

The result is therefore below 100 Ω.

Voltage Across Parallel Resistors

The voltage across every branch of a parallel circuit is the same.

V1 = V2 = V3 = Vin

If a 12 V supply is connected across several parallel resistors, each resistor has 12 V across it.

Branch Current

The current through each resistor can be calculated using Ohm's law:

I = V / R

Therefore:

I1 = V / R1

I2 = V / R2

I3 = V / R3

The total current is the sum of all branch currents.

IT = I1 + I2 + I3 + ...

Parallel Current Calculator

Example — Branch Currents

Suppose 100 Ω and 200 Ω resistors are connected across a 10 V supply.

I1 = 10 / 100

I1 = 0.1 A

I2 = 10 / 200

I2 = 0.05 A

The total current is:

IT = 0.1 + 0.05

IT = 0.15 A

Therefore, the supply must provide 150 mA.

Power Dissipation

Each parallel resistor dissipates power according to:

P = V² / R

Alternatively:

P = V × I

The total circuit power is the sum of the power dissipated by all branches.

PT = P1 + P2 + P3 + ...

Parallel Resistor Power Calculator

Two Equal Resistors in Parallel

When two identical resistors are connected in parallel, the equivalent resistance is half the value of either resistor.

RT = R / 2

For example:

R1 = 1 kΩ
R2 = 1 kΩ

RT = 1 kΩ / 2

RT = 500 Ω

Three Equal Resistors in Parallel

For three identical resistors:

RT = R / 3

For example, three 1 kΩ resistors produce:

RT = 1000 / 3

RT ≈ 333.33 Ω

Parallel Resistors for Higher Power

Multiple resistors can be connected in parallel to distribute power dissipation.

For example, several equal resistors can share the total current, provided that the resistors are suitably matched and have appropriate power ratings.

The current sharing will not necessarily be perfectly equal when resistors have different resistance values or tolerances.

Creating a Non-Standard Resistance

Parallel resistors can be used to obtain a resistance value that is not available as a single resistor.

For two resistors:

RT = (R1 × R2) / (R1 + R2)

For example, two 1 kΩ resistors in parallel produce 500 Ω.

Parallel Resistors and Current Sharing

The resistor with the lowest resistance carries the greatest current when the same voltage is applied across all branches.

I = V / R

Therefore, reducing a resistor's resistance increases its branch current.

Parallel Resistors in Power Supplies

Parallel resistor networks can be used in power circuits for load balancing, current sensing arrangements, discharge circuits and other applications.

The resistor power rating and maximum operating temperature should always be considered.

Parallel Resistors and Voltage

Unlike series resistors, parallel resistors do not divide the supply voltage between themselves.

Every branch has the same voltage:

V1 = V2 = V3 = Vin

The current divides between the branches.

Series vs Parallel Resistors

Common Applications

• Current sharing
• Power resistor networks
• Load networks
• Creating non-standard resistance values
• Voltage and current sensing
• Bias networks
• Termination networks
• Discharge circuits

Common Mistakes

• Adding parallel resistances directly.
• Forgetting that the voltage is the same across every branch.
• Forgetting that lower resistance means higher branch current.
• Ignoring individual resistor power dissipation.
• Using resistors with inadequate power ratings.
• Ignoring resistor tolerance when accurate current sharing is required.
• Accidentally wiring resistors in series instead of parallel.

Key Points

• Parallel resistors share the same voltage.
• Current divides between the branches.
• Total current is the sum of the branch currents.
• Equivalent resistance is lower than the smallest individual resistor.
• Two equal resistors in parallel have half the resistance of one resistor.
• Power is dissipated independently by each resistor.
• Parallel resistors can be used to share current and power.
• Resistor tolerance affects current sharing.