Circuit Homework: Find R for Switch Closed/Not Closed

[ianb]

Homework Statement

http://img514.imageshack.us/img514/1223/questionju1.jpg

Homework Equations

Parallell: \frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}

Series: R_{eq} = R_{1} + R_{2}

The Attempt at a Solution

Part 1 - When the switch is not closed:

R_{eq_2} = R + ((90+10)^{-1} + (90+10)^{-1})^{-1}
R_{eq_1} = R + 50

Part 2 - When the switch is closed:

R_{eq_2} = R + (90^{-1} + 10^{-1})^{-1} + (90^{-1} + 10^{-1})^{-1}
R_{eq_2} = R + 18

Since R_{eq_1} = 2R_{eq_2}, then

R + 50 = 2(R + 18)
R + 50 = 2R + 36
R = 14

The answer in the back, though, is 24. What have I done wrong?

 

[Mindscrape]

Good question, it looks to me like you did it right. Are you sure you didn't make a numerical error (this part looks okay too, though I didn't actually calculate)? How trustworthy are the answers in your book?

 

[ianb]

Thanks, mindscrape. I suppose the book could have misprinted the answer. One more thing, though, if you don't mind:

When the switch is closed, I calculated two parallel circuits. Are these two circuits, in turn, parallel to each other, or in series to each other (like I did above)?

 

[mlowery]

When the switch closes, it creates a node between the four resistors. The resulting parallel connections will be in series with each other - the way you calculated it.