Parallel Circuit

When two or more resistors are connected across a common point so that same current flows through different paths they are said to be connected in parallel. Suppose three resistors R₁, R₂ and R₃ are joined in parallel as shown in figure and let the potential difference applied across point A and B be V.

Let I be the current reaching point A from the battery and I₁, I₂ and I₃ be the current passing through resistors R₁, R₂ and R₃ respectively. Here it is clear that total current:

              I    =    I₁    +    I₂    +    I₃   (1)

According to Ohm’s law

              V   =    I₁R₁    =    I₂R₂    =    I₃R₃

    or       I₁    =    ,    I₂   =       and   I₃ =    

If R_p is the resultant resistance of the parallel circuit, then

              V    =    IR_p

    or       I    =    

By putting the values of I, I₁, I₂ and I₃ in equation (1), we get

    or       

       So, when the resistors are joined in parallel the reciprocal of total resistance of a number of resistors is equal to the sum total of the reciprocal of all the individual resistors.

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