Posted by **gita** on Sunday, September 8, 2013 at 1:54am.

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.

1) small resistance (ohm)

2) large resistance (0hm)

- Physics -
**Graham**, Sunday, September 8, 2013 at 4:07am
Given:

Series Resistance: S = 783.4 Ω

Parallel Resistance: P = 171.3 Ω

Let the resistances be r and q.

S = r + q

P = rq/(r + q)

.: rq = SP

and S = r + SP/r

.: r^2 - Sr + SP = 0

By symmetry if r is one root of the quadratic then q is the other. Let r be the lesser.

r = (S-√(S^2-4SP))/2

q = (S+√(S^2-4SP))/2

- Physics -
**Devron**, Sunday, September 8, 2013 at 9:27am
I solved a problem exactly like this the other day, but I made a math mistake; I should have checked my math.

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

use the quadratic equation and solve for R

R=[-b + or - sqrt*(b^2-4ac)]/2a

a=1, b=-783.4, and c=1.342 x 10^5

R=[-(-783.4) + or - sqrt*((-783.4)^2-4(1)(1.342 x 10^5)]/2(1)

R=[783.4 + or - (6.1372 x 10^5-5.368 x 10^5)]/2

R=[783.4 + or - sqrt*(7.6916 x 10^4)]/2

R=(783.4-277.3/2) or (783.4+277.3/2)

R=253.05Ω or R=530.35Ω

## Answer this Question

## Related Questions

- physics - Two resistors connected in series have an equivalent resistance of 783...
- physics - Two resistors connected in series have an equivalent resistance of 790...
- Physics - A 5.0 Ω resistor, a 9.0 Ω resistor, and a 10.0 Ω ...
- Physics - A 9.00 V storage battery is connected to three resistors, 4.25 Ω...
- physics (please check) - A total resistance of 3 ohms is to be producd by ...
- Physics - A)Two identical resistors are connected in parallel across a 30-V ...
- Physics - A)Two identical resistors are connected in parallel across a 30-V ...
- Physics - Three resistors having the same resistance value are wired in parallel...
- Physics - Consider the circuit shown in the figure below. Use the following as ...
- physics - A 14-Ω loudspeaker, a 9.0-Ω loudspeaker, and a 3.2-Ω ...