Final answer:
To find the resistance R2 in a circuit with parallel resistors where RT is 2 ohms and R1 is 6 ohms, use the parallel resistance equation and solve for R2, which results in a 3 ohm resistance for R2.
Step-by-step explanation:
The resistance of the second resistor, denoted as R2, in a parallel circuit can be calculated using the formula for two parallel resistors. Given that the total resistance, RT, is 2 ohms, and the first resistor, R1, is 6 ohms, the equation representing the total resistance of two parallel resistors is:
\( \frac{1}{RT} = \frac{1}{R1} + \frac{1}{R2} \)
Substituting the given values and solving for R2 yields:
\( \frac{1}{2} = \frac{1}{6} + \frac{1}{R2} \)
\( \frac{1}{R2} = \frac{1}{2} - \frac{1}{6} \)
\( \frac{1}{R2} = \frac{3}{6} - \frac{1}{6} \)
\( \frac{1}{R2} = \frac{2}{6} \)
\( R2 = \frac{6}{2} = 3 \ Ω \)
So, the resistance of R2 is 3 ohms.