Figure 2.30

← Back to Fundamentals of Electric Circuits Overview Figure 2.30

where Req is the equivalent resistance of the resistors in parallel:

$$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \tag{2.36}$$

or

$$\frac{1}{R_{\text{eq}}} = \frac{R_1 + R_2}{R_1 R_2}$$

or

$$R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2} \tag{2.37}$$

Thus,

The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.

It must be emphasized that this applies only to tw o resistors in parallel. From Eq. (2.37), if R¹ = R2 then Req = R1/R2.

We can extend the result in Eq. (2.36) to the general case of a circuit with N resistors in parallel. The equivalent resistance is

$$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_N}$$

(2.38)

Note that Req is always smaller than the resistance of the smallest resistor in the parallel combination. If R¹ = R² = ⋯=RN = R, then

$$R_{\text{eq}} = \frac{R}{N} \tag{2.39}$$