# Finding an unknown resistance in an Electric Circuit

1. Jul 25, 2010

### mlostrac

1. The problem statement, all variables and given/known data
When connected in series to a 110-V line, two resistors use one-fourth the power
that is used when they are connected in parallel. If one resistor is
2.0 kΩ, what is the resistance of the other?

2. Relevant equations
1/Rt = 1/R1 +1/R2 (total resistance in parallel)
Rt = R1 + R2 (resistance in series)

Power = Current x Voltage

3. The attempt at a solution

So far my attempts have fizzled, ending with negative numbers.

Heres what I did:
1) Set the two hypothetical circuits (series and parallel) equal to eachother by isolating the power:

P1 = 110^2/0.25(R1+R2)
P2 = 110^2(R1+R2)

And then isolating for R2 and solving (since we have R1 = 2000 ohms)

I ended up doing the quadratic equation and getting two negative numbers...

Any help would be appreciated :)

2. Jul 25, 2010

### kuruman

Can you show why it this true?
The term R1+R2 must be in the denominator.

Anyway, I suggest that you work this symbolically. Find expressions

Pseries = V2/Req,series
Pparallel = V2/Req,parallel
then take the ratio and say
Pseries/Pparallel = 1/4.