Question

the total resistance r of a certain circuit is given by the following formula. r = (1/r1 + 1/r2)^(-1)+r3. find r if r1 = 2, r2 = 7, and r3 = 3. r = enter a fraction, integer, or exact decimal. do not approximate.

Explanation:

Step1: Calculate $\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{2}+\frac{1}{7}=\frac{7 + 2}{14}=\frac{9}{14}$

Step2: Calculate $(\frac{1}{R_1}+\frac{1}{R_2})^{-1}$

$(\frac{1}{R_1}+\frac{1}{R_2})^{-1}=(\frac{9}{14})^{-1}=\frac{14}{9}$

Step3: Calculate $R$

$R = (\frac{1}{R_1}+\frac{1}{R_2})^{-1}+R_3=\frac{14}{9}+3=\frac{14 + 27}{9}=\frac{41}{9}$

Answer:

$\frac{41}{9}$