Question

PLEASE HELP!!

Rewrite the equation to represent the resistance of resistor 2, R2, in terms of RT and R1; see image below :

Answer 1

Rewriting the equation, it is found that the resistance $R_2$ is given by:

$R_2 = \frac{R_TR_1}{R_1 - R_T}$

The equation given for $R_T$ as function of $R_1$ and $R_2$ is:

$R_T = \frac{R_1R_2}{R_1+R_2}$

Applying cross multiplication:

$R_TR_1 + R_TR_2 = R_1R_2$

$R_1R_2 - R_TR_2 = R_TR_1$

$R_2(R_1 - R_T) = R_TR_1$

$R_2 = \frac{R_TR_1}{R_1 - R_T}$

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