Equivalent resistance of resistors in parallel (18-20)

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Question

Equivalent resistance of $N$ resistors in parallel

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Review

Equation 18-20 tells us that by combining resistors in parallel, we create a circuit with a smaller equivalent resistance than any of the individual resistors. For the special case of two identical resistors $R$ in parallel, the equivalent resistance is given by

$\frac{1}{R_{\mathrm{equiv}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$ so $R_{\mathrm{equiv}} = \frac{R}{2}$

The equivalent resistance of two identical resistors in parallel is onehalf that of each individual resistor.