Parallel Circuit Essentials: 7 Steps to Calculate Resistance, Voltage & Current

Table of Contents

A parallel circuit allows electricity to flow through multiple branches while keeping the same voltage across each branch. It differs from series circuits in that currents divide among branches, and total resistance is calculated using a specific parallel circuit formula. Understanding what a parallel circuit is, how voltage behaves in parallel circuit, and how to find current in a parallel circuit are essential for PCB/PCBA design. This article includes real parallel circuit examples, parallel circuit diagrams, and step-by-step methods for calculating total resistance, voltage, and current.

1. Fundamental Principles of Parallel Circuit

Voltage in Parallel Circuit

In any parallel circuit, the voltage across each branch equals the supply voltage. For example, if a 12 V supply is connected to three resistors in parallel, each resistor sees the full 12 V. This characteristic makes parallel circuits ideal in PCB/PCBA scenarios where consistent voltage across multiple components is necessary.

Current in Parallel Circuit

The total current in a parallel circuit is the sum of the current in each branch. Each branch current is given by Ohm’s law: I_branch = V / R_branch. Branches with lower resistance draw more current. Knowing how to calculate current in a parallel circuit helps in trace sizing, thermal design, and load balancing.

Total Resistance in Parallel Circuit

The total or equivalent resistance in a parallel circuit is always less than the smallest individual branch resistance. Use the parallel circuit formula:

1 / R_total = 1 / R₁ + 1 / R₂ + … + 1 / Rₙ
For two resistors: R_total = (R₁ × R₂) / (R₁ + R₂)

Parallel Circuit Diagram

Hcjmpcba Parallel Circuit Diagram

Diagram: resistors in a parallel circuit, each branch connected across the same voltage supply

2. Step-by-Step: How to Calculate Resistance in a Parallel Circuit

List each branch resistance R₁, R₂, …, Rₙ.
Compute the reciprocal sum: 1 / R₁ + 1 / R₂ + … + 1 / Rₙ.
Take the reciprocal of that sum to find R_total.
If the supply voltage V is known, compute total current: I_total = V / R_total.
Compute each branch’s current: I_i = V / R_i.

3. Parallel Circuit Examples

Example 1 – Two Resistors in Parallel

Let R₁ = 100 Ω, R₂ = 200 Ω; supply voltage V = 12 V.
Then:

1 / R_total = 1/100 + 1/200 = 0.01 + 0.005 = 0.015
R_total = 66.67 Ω
I_total = 12 V / 66.67 Ω ≈ 0.18 A
Branch currents: I₁ = 12 V / 100 Ω = 0.12 A, I₂ = 12 V / 200 Ω = 0.06 A

Example 2 – Three Resistors in Parallel

Let R₁ = 100 Ω, R₂ = 150 Ω, R₃ = 300 Ω; supply voltage V = 9 V.

1 / R_total = 1/100 + 1/150 + 1/300 = 0.01 + 0.006667 + 0.003333 = 0.020
R_total ≈ 50 Ω
I_total = 9 V / 50 Ω = 0.18 A
Branch currents: I₁ = 9/100 = 0.09 A, I₂ = 9/150 = 0.06 A, I₃ = 9/300 = 0.03 A

4. Series vs Parallel Circuits: When to Use Which

Feature	Series Circuit	Parallel Circuit
Voltage across components	Divided among components	Same for each branch
Current through components	Same through all	Different currents in each branch
Total Resistance	Sum of resistances	Less than the smallest branch resistance
Failure behavior	If one component fails, series breaks	If one branch fails, others still work

5. Practical Considerations in PCB / PCBA Design

Routing & Trace Width: ensure branches with higher current have wider traces; shared nodes must handle combined current.
Component Tolerances: resistor tolerances (1 %, 0.1 %) impact current distribution in parallel circuits.
Heat Dissipation: larger currents in branches generate heat; use thermal vias, copper pours, heatsinks.
EMI / Noise: ground plane layout, shielding, symmetric routing to reduce interference.
Safety & Protection: fuse protection, proper spacing, isolate potential short branches in design.

6. FAQ

Q1: What is the parallel circuit formula?

The formula for total resistance in a parallel circuit is: 1 / R_total = 1 / R₁ + 1 / R₂ + … + 1 / Rₙ. For two resistors: R_total = (R₁ × R₂) / (R₁ + R₂).

Q2: How do you find current in a parallel circuit?

First compute R_total, then I_total = V / R_total. Each branch current is I_branch = V / R_branch.

Q3: Can voltage drop occur in a parallel circuit?

In idealized circuits, all branches share the same voltage. In real PCB/PCBA designs, trace resistance or connection losses may introduce slight voltage drops.

Q4: What if one branch fails?

If a branch opens (fails), it stops conducting; other branches still function normally. Total current drops; total resistance increases accordingly.

Q5: How to calculate resistance in circuits with both series and parallel parts?

Break down the circuit: calculate equivalent resistance of each parallel group, then combine with series parts using standard formulae for series-parallel circuits.