Electrical Engineering ⇒ Topic : Parellel combination of resistors

PARALLEL COMBINATION OF RESISTORS

In Figure (a), two resistors R₁ and R₂ are connected in parallel at the terminals A-B. A voltage source of V volt is connected across A-B. The current through R₁ and R₂ be I₁ and I₂, respectively. The total current I is given by

                                   I = I₁ + I₂

Since           V_A - V_B = V

                                                                              FIGURE (A)

                                             ..................     (1)

Now, let the parallel combination of resistors be replaced by a single resistor R such that the same current I flows through it which is given below.

                                                                                                                                                                       ....................  (2)

From Eqs. (1) and (2), we have

If n resistors R₁, R₂, ..........., R_n are connected in parallel, their equivalent resistance R is given by