The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.
In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]
We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.
To rewrite the equation, we do as follows:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]
Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
Learn more about the rewriting of equations at
https://brainly.com/question/24272167
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For the complete question, refer to the attachment.
