Resistors in Parallel
The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
Learning Objective

Calculate the total resistance in the circuit with resistors connected in parallel
Key Points
 The total resistance in a parallel circuit is less than the smallest of the individual resistances.
 Each resistor in parallel has the same voltage of the source applied to it (voltage is constant in a parallel circuit).
 Parallel resistors do not each get the total current; they divide it (current is dependent on the value of each resistor and the number of total resistors in a circuit).
Terms

parallel
An arrangement of electrical components such that a current flows along two or more paths.

resistance
The opposition to the passage of an electric current through that element.
Full Text
Overview
Resistors in a circuit can be connected in series or in parallel. The total resistance of a combination of resistors depends on both their individual values and how they are connected.
Resistors in Parallel
Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it .
Resistors in Parallel
A parallel connection of resistors.
Each resistor draws the same current it would if it were the only resistor connected to the voltage source. This is true of the circuitry in a house or apartment. Each outlet that is connected to a appliance (the "resistor") can operate independently, and the current does not have to pass through each appliance sequentially.
Ohm's Law and Parallel Resistors
Each resistor in the circuit has the full voltage . According to Ohm's law, the currents flowing through the individual resistors are
Parallel resistors
Three resistors connected in parallel to a battery and the equivalent single or parallel resistance.
Substituting the expressions for individual currents gives:
or
This implies that the total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances. Therefore, for every circuit with
This relationship results in a total resistance that is less than the smallest of the individual resistances. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower.
Each resistor in parallel has the same full voltage of the source applied to it, but divide the total current amongst them. This is exemplified by connecting two light bulbs in a parallel circuit with a 1.5V battery. In a series circuit, the two light bulbs would be half as dim when connected to a single battery source. However, if the two light bulbs were connected in parallel, they would be equally as bright as if they were connected individually to the battery. Because the same full voltage is being applied to both light bulbs, the battery would also die more quickly, since it is essentially supplying full energy to both light bulbs. In a series circuit, the battery would last just as long as it would with a single light bulb, only the brightness is then divided amongst the bulbs.
Key Term Reference
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 Ohm's law
 Appears in these related concepts: Ohm's Law, Root Mean Square Values, and Resistors in AC Circuits
 battery
 Appears in these related concepts: Fuel Cells, The Battery, and Sources of EMF
 circuit
 Appears in these related concepts: Combinations of Capacitors: Series and Parallel, Microwaves, and Maxwell's Equations
 conservation
 Appears in these related concepts: Conservation of Mechanical Energy, Museums and Private Collections, and Linear Momentum
 current
 Appears in these related concepts: Reporting LongTerm Liabilities, Magnetic Force Between Two Parallel Conductors, and The Junction Rule
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 inverse
 Appears in these related concepts: Inverse Functions, The Law of Universal Gravitation, and Hyperbolic Functions
 ohm
 Appears in these related concepts: Resonance in RLC Circuits, Poiseuille's Equation and Viscosity, and Current and Voltage Measurements in Circuits
 resistor
 Appears in these related concepts: Impedance, The Loop Rule, and Introduction and Importance
 series
 Appears in these related concepts: Combination Circuits, Resisitors in Series, and The General Term of a Sequence
 voltage
 Appears in these related concepts: The Nernst Equation, Electric Potential Due to a Point Charge, and Principles of Electricity
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