2 Resistors in Parallel versus in Series

[mlostrac]

Homework Statement

Two resistors when connected in series to a 110 V line 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?

Homework Equations

V=IR

The Attempt at a Solution

v=ir

110=i(2000+x)

110=1/4(2000+x)

440=2000+x

x=440-2000

x=-1560

snce x= 1560

the value of another resistance is 1.56 kilo ohm

Did I do that right?

 

[Mindscrape]

Not quite. Okay, your series formula is fine. But now you have to get the power for the resistors in series. P=I^2 R and P=V^2/R.

Now that you have the power for the series resistors, find the power for the resistors if they were in parallel. 110=i*Req again, but different Req this time.

 

[mlostrac]

Can I just cancel the V's out and solve like this:

R2 + 2000 = 2*(2000*R2)/(2000 + R2)

Which looks like it would require the quadratic eqn