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Parallel resistance
Storyboard

When the resistors are connected in parallel, they are all exposed to the same potential difference which, by Ohm's law, generates different currents. The total current is the sum of the partial currents, so the total resistance is the inverse of the sum of the inverse of the individual resistances.

>Model

ID:(1397, 0)


Parallel resistors (Diagram)
Definition

The diagram representing resistors connected in parallel has the following form:
 

ID:(7861, 0)


Parallel resistance (2)
Description

When the resistors are connected in parallel, they are all exposed to the same potential difference which, by Ohm's law, generates different currents. The total current is the sum of the partial currents, so the total resistance is the inverse of the sum of the inverse of the individual resistances.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$I$
I
Current
A
$I_1$
I_1
Current 1
A
$I_2$
I_2
Current 2
A
$\Delta\varphi$
Dphi
Potential difference
V
$R_1$
R_1
Resistance 1
Ohm
$R_2$
R_2
Resistance 2
Ohm
$R_p$
R_p
Resistance in Parallel
Ohm

Calculations

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Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

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Equations

Examples


(ID 16032)


(ID 16021)

The inverse of the resistance in Parallel ($R_p$) is equal to the sum of the inverses of the resistance 1 ($R_1$) and the resistance 2 ($R_2$). This relationship is expressed as:

$\displaystyle\frac{1}{ R_p }=\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }$

(ID 16006)

By the principle of conservation of electric charge, the current ($I$) is equal to the sum of the current 1 ($I_1$) and the current 2 ($I_2$). This relationship is expressed as:

$ I = I_1 + I_2 $

(ID 16009)

Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:

$ \Delta\varphi = R I $

(ID 3214)

Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:

$ \Delta\varphi = R I $

(ID 3214)

Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:

$ \Delta\varphi = R I $

(ID 3214)

ID:(1397, 0)