Question

which of the following formulas would be used to combine two parallel resistors with unlike values?

(r1 × r2) × (r1 + r2)
r1 + r2 / r1 × r2
(r1 × r2) / r1 + r2
r1 + r2 / r1 + r2

Explanation:

Step1: Recall the formula for parallel resistors

For two parallel resistors \(R_1\) and \(R_2\), the equivalent resistance \(R_{eq}\) is given by \(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\).

Step2: Derive the formula

Cross - multiply: \(\frac{1}{R_{eq}}=\frac{R_2 + R_1}{R_1R_2}\), then \(R_{eq}=\frac{R_1R_2}{R_1 + R_2}\).

Answer:

\((R1\times R2)/(R1 + R2)\) (the third option)