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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:(2120, 0)

Iframe

>Top

ID:(16033, 0)

Top

>Top

Parameters

$R_1$

R_1

Resistance 1

Ohm

$R_2$

R_2

Resistance 2

Ohm

$R_3$

R_3

Resistance 3

Ohm

$R_p$

R_p

Resistance in Parallel

Ohm

Variables

$I$

I

Current

A

$I_1$

I_1

Current 1

A

$I_2$

I_2

Current 2

A

$I_3$

I_3

Current 3

A

$\Delta\varphi$

Dphi

Potential difference

V

Calculations

• Alternative method
• Traditional method
• Strategy
• 2D
• 3D

Equation

Number

First, select the equation: to , then, select the variable: to

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Calculations

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable Given Calculate Target : Equation To be used

Equations

ID:(16022, 0)

Equation

>Top, >Model

The inverse of the resistance in Parallel ($R_p$) is equal to the sum of the inverses of the resistance 1 ($R_1$), the resistance 2 ($R_2$) and the resistance 3 ($R_3$). This relationship is expressed as:

$\displaystyle\frac{1}{ R_p }=\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }+\displaystyle\frac{1}{ R_3 }$

Conditions

Variables

$R_1$

Resistance 1

$Ohm$

5500

$R_2$

Resistance 2

$Ohm$

5501

$R_3$

Resistance 3

$Ohm$

5502

$R_p$

Resistance in Parallel

$Ohm$

5499

Relation

ID:(16007, 0)

Equation

>Top, >Model

By the principle of conservation of electric charge, the current ($I$) is equal to the sum of the current 1 ($I_1$), the current 2 ($I_2$) and the current 3 ($I_3$). This relationship is expressed as:

$I = I_1 + I_2 + I_3$

Conditions

Variables

$I$

Current

$A$

5483

$I_1$

Current 1

$A$

9677

$I_2$

Current 2

$A$

9678

$I_3$

Current 3

$A$

10484

Relation

ID:(16010, 0)

Equation

>Top, >Model

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:

$\Delta\varphi = R_p I$

$\Delta\varphi = R I$

Conditions

Variables

$I$

Current

$A$

5483

$\Delta\varphi$

Potential difference

$V$

5477

$R$

$R_p$

Resistance in Parallel

$Ohm$

5499

Relation

Development

None

ID:(3214, 1)

Equation

>Top, >Model

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:

$\Delta\varphi = R_1 I_1$

$\Delta\varphi = R I$

Conditions

Variables

$I$

$I_1$

Current 1

$A$

9677

$\Delta\varphi$

Potential difference

$V$

5477

$R$

$R_1$

Resistance 1

$Ohm$

5500

Relation

Development

None

ID:(3214, 2)

Equation

>Top, >Model

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:

$\Delta\varphi = R_2 I_2$

$\Delta\varphi = R I$

Conditions

Variables

$I$

$I_2$

Current 2

$A$

9678

$\Delta\varphi$

Potential difference

$V$

5477

$R$

$R_2$

Resistance 2

$Ohm$

5501

Relation

Development

None

ID:(3214, 3)

Equation

>Top, >Model

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:

$\Delta\varphi = R_3 I_3$

$\Delta\varphi = R I$

Conditions

Variables

$I$

$I_3$

Current 3

$A$

10484

$\Delta\varphi$

Potential difference

$V$

5477

$R$

$R_3$

Resistance 3

$Ohm$

5502

Relation

Development

None

ID:(3214, 4)