By S. Hussain Ather • Updated Mar 24, 2022

Electrical circuits are organized either in series or in parallel. In a series connection, each element lies on the same path, so the same current flows through every component one after another. In a parallel arrangement, each component has its own branch, and the current can split and recombine at junctions.

Parallel Circuit Diagram

A typical parallel diagram shows the positive terminal of a voltage source (+) connected to one node and the negative terminal (–) to another. From the positive node, the current splits into multiple branches, each ending at the negative node. Kirchhoff’s Current Law guarantees that the total current entering a junction equals the total current leaving it, while Kirchhoff’s Voltage Law ensures that the sum of voltage drops around any closed loop is zero.

Parallel Circuit Characteristics

In parallel circuits, the voltage across every branch is identical, equal to the source voltage. The current, however, divides among the branches in proportion to their conductance (the reciprocal of resistance). Thus, the branch with the lowest resistance draws the most current, and the branch with the highest resistance draws the least.

TL;DR

Parallel circuits keep voltage constant across all branches while allowing current to flow through multiple paths simultaneously. Ohm’s Law applies to each branch, and series‑parallel networks can be analyzed by combining both series and parallel rules.

Parallel Circuit Examples

To compute the total resistance of resistors in parallel, use the reciprocal formula:

\(\displaystyle \frac{1}{R_{\text{total}}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\dots+\frac{1}{R_n}\)

For example, with resistors of 5 Ω, 6 Ω, and 10 Ω:

1. \(\displaystyle \frac{1}{R_{\text{total}}}=\frac{1}{5}+\frac{1}{6}+\frac{1}{10}\)
2. \(\displaystyle \frac{1}{R_{\text{total}}}=\frac{6}{30}+\frac{5}{30}+\frac{3}{30}=\frac{14}{30}\)
3. \(\displaystyle R_{\text{total}}=\frac{30}{14}=\frac{15}{7}\approx 2.14\,\text{Ω}\)

Once the resistance is known, apply Ohm’s Law \(V=IR\) to find currents in each branch, remembering that the voltage across each resistor equals the source voltage.

Parallel vs. Series Circuit

Key differences:

• Series: Constant current, voltage drops across each component, total resistance is the sum of individual resistances.
• Parallel: Constant voltage, current divides among branches, total conductance is the sum of individual conductances.

In a series network, a single open circuit stops the entire current flow. In contrast, a parallel network keeps the other branches operating even if one opens.

Series‑Parallel Circuit

Real‑world circuits often combine both configurations. For example, consider resistors R1–R6 arranged so that R1 and R2 are parallel (forming R5), and R3 and R4 are parallel (forming R6). These two combined resistances are then connected in series:

1. \(\displaystyle \frac{1}{R_5}=\frac{1}{1}+\frac{1}{5}\) → \(R_5=\frac{5}{6}\,\text{Ω}\)
2. \(\displaystyle \frac{1}{R_6}=\frac{1}{7}+\frac{1}{2}\) → \(R_6=\frac{14}{9}\,\text{Ω}\)
3. \(R_{\text{total}}=R_5+R_6=\frac{5}{6}+\frac{14}{9}=\frac{43}{18}\,\text{Ω}\approx 2.38\,\text{Ω}\)

With a 20 V source, the total current is \(I_{\text{total}}=V/R_{\text{total}}\approx 8.37\,\text{A}\). The voltage drop across each combined resistor is then calculated using Ohm’s Law, and the individual branch currents follow from their respective resistances.

These principles allow engineers to design reliable, efficient power systems that maintain steady voltage while providing multiple pathways for current, a fundamental requirement for residential and industrial electrical infrastructure.