Combination of resistors - Parallel combination of Resistors

 PARALLEL COMBINATION OF RESISTORS

In parallel combination of resistors, resistances are connected in such a way that the same voltage is applied across each resistor.

And depending upon the value of resistors, the current gets divided among them. i.e current flowing through each resistance is different.

Let R₁, R₂ and R₃ be the resistors connected in parallel as shown in the figure. And the current flowing through each resistance be I₁, I₂ and I₃.

The total current is given by

I = I₁ + I₂ + I₃   -------------------------- (1)

According to Ohm’s law

V=IR

I = V/R

Now, I₁ = V/R₁

I₂ = V/R₂

I₃ = V/R₃

Therefore, equation (1) becomes

        V/R = V/R₁ + V/R₂ + V/R₃

        V/R = V (1/R₁ + 1/R₂ + 1/R₃)

        1/R = (1/R₁ + 1/R₂ + 1/R₃)

Thus we can say that in parallel combination of resistors the equivalent resistance of the circuit decreases.

NOTE:

Case 1: If all resistors connected in circuit are of same value i.e

R₁ = R₂ = R₃ = R

1/R _parallel = 1/R + 1/R + 1/R

1/R _parallel = 3/R

                R _parallel = R/3

Hence if ‘n’ number of resistances connected in parallel then

                R _parallel = R/n

And the current flowing through each resistance is given by

                i’ = i/n

Case 2: If only two resistors are connected in parallel then the equivalent resistance is given by

                     R_p = R1R2/(R1+R2)

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