Question

Two resistors when connected in series have a total resistance of 40 ohms and when connected in parallel

has a total resistance of 7.5 ohms. Find the value of each resistor in ohm 

Answer 1

Write the formulas:

$$R_{p}=\frac{R_1R_2}{R_1+R_2}=7.5.\\\space\\ R_{s}=R_1+R_2=40.\\\space\\ R_1=40-R_2,\\\space\\ 7.5=\frac{(40-R_2)R_2}{40},\\\space\\ R_2^2-40R_2+300=0,\\\space\\ R_2=10\Omega, R_1=30\Omega;\\ R_1=10\Omega, R_2=30\Omega.$$