Resistors in Parallel - Parallel Connected Resistors

In a parallel circuit, the same voltage is applied across all components and the total current is the sum of all the individual branch currents.

Resistors parallel

Laws of parallel connection

The voltage is the same everywhere in a parallel connection.

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The total current is the sum of all partial currents:

I_t =  I₁  +  I₂ + … +  I_n         (1)

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Determination of the total resistance:

I_t   =  I₁  +  I₂ + … +  I_n          Eq.(1) divided by V
V       V       V           V

according to the Law of Ohm follows

1      =      1   +   1   +    …   +     1  
R_t           R₁       R₂                      R_n 

Special case 1: All the resistors are of the same size

1      =    n       bzw.     R_t = R / n
R_t          R

Special case 2: Only 2 resistors are in parallel

1      =      1   +  1      =   R2 + R1
R_t             R₁     R₂          R2 * R1

Form reciprocal and it follows:

R_t   =   R2 *  R1    
            R1  +   R2