The correct formula to calculate the equivalent resistance of two resistors R1 and R2 when connected in parallel, is:
- (a)$$\begin{aligned}\frac{\text R_1 + \text R_2}{\text R_1\text R_2} \\[1em]\end{aligned}$$
- (b)$$\begin{aligned}\frac{\text R_1\text R_2}{\text R_1 + \text R_2} \\[1em]\end{aligned}$$
- (c)$$\begin{aligned}\frac{\text R_1 - \text R_2}{\text R_1\text R_2} \\[1em]\end{aligned}$$
- (d)$$\begin{aligned}\frac{\text R_1\text R_2}{\text R_1 - \text R_2} \\[1em]\end{aligned}$$
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$$\begin{aligned}\frac{\text R_1\text R_2}{\text R_1 + \text R_2} \\[1em]\end{aligned}$$
Reason — When two resistors are connected in parallel, the potential difference across each resistor is the same, while the current divides between the branches. For two resistors R1 and R2, the reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances i.e.,
$$\begin{aligned}\frac{1}{\text R} = \frac{1}{\text R_1} + \frac{1}{\text R_2} \\[1em] \Rightarrow \frac{1}{\text R} = \frac{\text R_1 + \text R_2}{\text R_1\text R_2} \\[1em] \Rightarrow \text R = \frac{\text R_1\text R_2}{\text R_1 + \text R_2} \\[1em]\end{aligned}$$