In electronics, the relationship among the resistances \( \mathrm{R}_{1} \) and \( \mathrm{R}_{2} \) of two resistors wired in a parallel circuit and their combined resistance R is described by the following formula. \( \frac{1}{\mathrm{R}}=\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}} \) Use this formula to find \( \mathrm{R}_{2} \), if the combined resistance R is 3 ohms and \( \mathrm{R}_{1} \) is 6 ohms. \( \mathrm{R}_{2}=\square \) ohms (Type an integer or a simplified fraction.)

To find \( R_{2} \), we can rearrange the formula for combined resistance in parallel circuits: \[ \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \] Plugging in the values we know: \[ \frac{1}{3} = \frac{1}{6} + \frac{1}{R_{2}} \] Subtract \( \frac{1}{6} \) from both sides: \[ \frac{1}{R_{2}} = \frac{1}{3} - \frac{1}{6} \] Finding a common denominator (which is 6), we get: \[ \frac{1}{3} = \frac{2}{6} \Rightarrow \frac{1}{R_{2}} = \frac{2}{6} - \frac{1}{6} = \frac{1}{6} \] Taking the reciprocal gives: \[ R_{2} = 6 \text{ ohms.} \] So, \( R_{2} = 6 \) ohms.