What is the difference between series and parallel circuits

In a series circuit every element shares a single path for charge flow. The current I is identical through each component, and the total voltage of the source is divided among them according to Ohm's law. The equivalent resistance is the sum of the individual resistances: $R_{eq}=R_1+R_2+\dots+R_n$. For example, three resistors of 2 Ω, 3 Ω, and 5 Ω connected in series to a 12 V battery give $R_{eq}=10\,\Omega$ and a current $I=V/R_{eq}=12/10=1.2\,\text{A}$. The voltage drops are then 2.4 V, 3.6 V, and 6.0 V respectively, adding back to 12 V.

Parallel Circuits

A parallel circuit provides multiple independent paths between the same two nodes. The voltage across each branch equals the source voltage, while the total current is the sum of the branch currents. The equivalent resistance follows $1/R_{eq}=1/R_1+1/R_2+\dots+1/R_n$. Using the same three resistors (2 Ω, 3 Ω, 5 Ω) in parallel across 12 V, we find $1/R_{eq}=0.5+0.333+0.2=1.033$ so $R_{eq}\approx0.97\,\Omega$. The total current is $I=12/0.97\approx12.4\,\text{A}$, with branch currents of 6 A, 4 A, and 2.4 A respectively, illustrating how parallel connections draw more current.

Key differences between series and parallel circuits:

• Current is the same in series, voltage is the same in parallel.
• Resistances add in series, reciprocals add in parallel.
• Series reduces total current, parallel increases total current.
• A break in a series path stops all flow; a break in one parallel branch leaves others operating.

Analyzing a circuit that contains both series and parallel sections:

1. 1Identify groups of components that are purely series or purely parallel.
2. 2Replace each identified group with its equivalent resistance.
3. 3Redraw the simplified circuit and repeat until only a single equivalent resistance remains.
4. 4Use Ohm's law with the source voltage to find the total current, then work backward to find individual branch currents and voltage drops.

Comparison of typical electrical quantities: