Resistances in Parallel and Series

 Resistances in electrical circuits are arranged in parallel or in series. The equivalent value of the resistances are calculated keeping in mind that the potential drop across resistances in parallel is the same while the potential drop across a number of resistances in series is additive.
Hence the equivalent resistance R_eq across 'n' resistors each having a resistance of R is given by the following formula:

                                                                Req =  å R = n

However, when there are n resistors of resistance R in series, then the reciprocal of the cumulative resistance is given by the sum of the reciprocals of the individual resistances. The following formula is used:

                                                            1/Req =  å 1/ R = n/R

If the values of the resistances are not all equal, then the formulas are given by:

                                       Req =  å  R_i=R₁+R₂+R₃+...+R_i+...R_n  ( for i = 1 ... n)

and when they are parallel then the equivalent resistance is:

                          1/Req =  å 1 / R_i =1/R₁+ 1/R₂+ 1/R₃ +...+ 1/R_i + ... 1/R_n ( for i = 1 ... n)
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Quiz

What is the equivalent resistance in the circuit shown in the figure?

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