Question

Two resistors connected in series have an equivalent resistance of 783.4 Ω. When they are connected in parallel, their equivalent resistance is 171.3 Ω. Find the resistance of each resistor.
Ω (small resistance)
Ω (large resistance

Answer 1

Equation 1.)

R1+R2=783.4

Equation 2.)

R1*R2/(R1+R2)=Req=783.4

Substitute equation 1 into 2:

R1=783.4-R2

and

R1*R2/(R1+R2)=Req=171.3

(783.4-R2)*R2/783.4-R2+R2=171.3

R2^2-783.4R2=-1.342 x 10^5

R2^2 -783.4R2+1.342 x 10^5=0

(R2 -3.663 x 10^2)^2

R2=3.663 x 10^2 Ω

R1 + R2=783.4 Ω

R1=783.4 Ω-R2

R1=734.4Ω-3.663 x 10^2 Ω

R1=417.1 Ω