SOLUTION: Cristina found out that the total electrical resistance of R of two resistors connected in parallel is given by 1/R=1/R1+1/R2. The total resistance is 12.3 ohms. Let 2x-1=R1. A.

Algebra ->  Test  -> Lessons -> SOLUTION: Cristina found out that the total electrical resistance of R of two resistors connected in parallel is given by 1/R=1/R1+1/R2. The total resistance is 12.3 ohms. Let 2x-1=R1. A.       Log On


   

Question 570107: Cristina found out that the total electrical resistance of R of two resistors connected in parallel is given by 1/R=1/R1+1/R2. The total resistance is 12.3 ohms. Let 2x-1=R1.
A. Express the second resistance R2 as a function of x.
B. Find R2 if x is : ohms.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2FR=1%2FR1%2B1%2FR2.
The total resistance is 12.3 ohms. Let 2x-1=R1.
1%2F12.3=1%2F%282x-1%29%2B1%2FR2.
:
A. Express the second resistance R2 as a function of x.
1%2F12.3=1%2F%282x-1%29%2B1%2FR2
Lets simplify things here
Let a = R1 = (2x-1)
Let b = R2
Rewrite the equation to
1%2F12.3=1%2Fa + 1%2Fb.
Multiply thru by 12.3ab
12.3ab*1%2F12.3= 12.3ab*1%2Fa + 12.3ab*1%2Fb
cancel the denominators, results
ab = 12.3b + 12.3a
Get b in terms of a
ab - 12.3b = 12.3a
Factor out b on the left
b(a-12.3) = 12.3a
b = %2812.3a%29%2F%28%28a-12.3%29%29
Replace a with (2x-1), and b with R2
R2 = %2812.3%282x-1%29%29%2F%28%28%282x-1%29-12.3%29%29
:
R2 = %2824.6x-12.3%29%2F%282x-13.3%29; is R2 in terms of x
:
:
B. Find R2 if x is : ohms. You didn't give any value for x, you can find what that is and substitute it for x in the above, to find R2