Parallel Circuit
A parallel circuit is an electrical circuit in which components are connected across the same two nodes, providing multiple independent current paths each sharing the same voltage. The total resistance of a parallel combination is always less than the smallest individual resistance. Parallel wiring is used in household electrical systems so that each appliance receives the full supply voltage independently.
Key Formula
1/R_total = 1/R1 + 1/R2 + 1/R3
LaTeX: \dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}
| Symbol | Meaning | Unit |
|---|---|---|
| R_total | Total equivalent resistance | Ohm (Ω) |
| R₁, R₂, R₃ | Individual branch resistances | Ohm (Ω) |
Worked Example
Problem
Two resistors of 6 Ω and 12 Ω are connected in parallel to a 12 V supply. Find the total resistance and total current drawn.
Solution
Step 1: 1/R_total = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. So R_total = 4 Ω. Step 2: I_total = V / R_total = 12 / 4 = 3 A. Check: I₁ = 12/6 = 2 A; I₂ = 12/12 = 1 A; 2 + 1 = 3 A ✓
Answer
R_total = 4 Ω; I_total = 3 A
Current Distribution in a Three-Branch Parallel Circuit (12 V supply)
| Branch | Resistance (Ω) | Voltage (V) | Current (A) |
|---|---|---|---|
| Branch 1 | 4 | 12 | 3.0 |
| Branch 2 | 6 | 12 | 2.0 |
| Branch 3 | 12 | 12 | 1.0 |
| Total (combined) | 2 | 12 | 6.0 |
Interactive Tools
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Related Terms
Series Circuit
A series circuit is an electrical circuit in which all components are connected end-to-end along a single path, so the same current flows through each component. The total resistance equals the sum of individual resistances, and the supply voltage is divided among the components. If any component in a series circuit fails (open circuit), current through the entire circuit ceases.
Electrical Resistance
Electrical resistance is the opposition that a material offers to the flow of electric current, quantifying how much a conductor restricts charge flow for a given applied voltage. It depends on the material's resistivity, its length, and its cross-sectional area, and increases with temperature in most metals. Resistance is central to controlling current in circuits and forms the basis of Ohm's Law.
Electric Current
Electric current is the rate of flow of electric charge through a conductor, measured as the amount of charge passing a cross-section per unit time. It is the fundamental quantity that drives electrical circuits and powers all electronic devices. In metallic conductors, current arises from the drift of free electrons, while in electrolytes and plasma it involves the movement of ions.
From Greek "parallelos" meaning "beside one another", derived from "para" (beside) + "allelon" (of one another). The term was adopted into electrical engineering in the 19th century to describe components sharing common connection points.