[tex]R_2[/tex] is 3 ohms
In a circuit containing two resistors [tex]R_1[/tex] and [tex]R_2[/tex] connected together in parallel, the total resistance [tex]R_T[/tex] is given by;
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}[/tex] ---------(i)
Make [tex]R_2[/tex] subject of the formula;
=> [tex]\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}[/tex]
=> [tex]\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}[/tex]
=> [tex]{R_2} = \frac{R_TR_1}{R_1 - R_T}[/tex] ---------------(ii)
From the question,
[tex]R_1[/tex] = 6Ω
[tex]R_T[/tex] = 2Ω
Substitute these values into equation (ii) as follows;
=> [tex]{R_2} = \frac{2*6}{6 - 2}[/tex]
[tex]{R_2} = \frac{12}{4}[/tex]
[tex]R_2[/tex] = 3Ω
Therefore, the value of [tex]R_2[/tex] = 3 ohms or [tex]R_2[/tex] = 3Ω
