Solve
1/C=1/C1 + 1/C2 for C1
This multiple choice and the listed answers are:
a.)C1= CC2/(C2-C)
b.)C1= C-C2/C
c.)C1= C+C2/CC2
d.)C1= C+C2/C2
Show us your attempt to do the algebra. You won't learn a thing is you ask us to just do your work for you.
The first step would be to write
1/C1 = 1/C - 1/C2 = (C2 - C)/(C*C2)
The take the reciprocal of both sides.
Very nearly the same question was posted last night. Was it by you?
Yes, I am still having problems with this problem. I understand this part
1/C1 = 1/C - 1/C2
but I don't understand this part:
(C2 - C)/(C*C2)
Okay I understand it now I have to make them have the same denominators so I multiply 1/C by the numerator and denominator by C2 so it would be C2/(C2*C)
and the other part is 1/C2 times C which would be C/(C2*C) which would make the problem 1/C1= C2-C/(C2*C)
what do I do next?
Flip both fractions upside down, as i indicated earlier.
You will be using the fact that if a/b = c/d, then b/a = d/c
You will end up with the equation for C1
To solve the equation 1/C = 1/C1 + 1/C2 for C1, we can rearrange the equation to isolate C1 on one side. Here's how you can do it:
1. Start with the equation: 1/C = 1/C1 + 1/C2
2. Since C1 is in the denominator term, we need to combine the fractions on the right side into a single fraction. The common denominator will be C1 * C2.
Multiply the first term, 1/C1, by C2/C2:
1/C1 * C2/C2 = C2/(C1 * C2)
Multiply the second term, 1/C2, by C1/C1:
1/C2 * C1/C1 = C1/(C1 * C2)
3. Combine the fractions on the right side:
C2/(C1 * C2) + C1/(C1 * C2) = (C2 + C1)/(C1 * C2)
4. Now that the right side is a single fraction, we can set it equal to 1/C and solve for C1:
(C2 + C1)/(C1 * C2) = 1/C
Cross-multiply:
C * (C2 + C1) = (C1 * C2) * 1
Distribute C on the left side:
C * C2 + C * C1 = C1 * C2
Rearrange the terms to isolate C1:
C * C1 - C1 * C2 = -C * C2
Factor out C1 on the left side:
C1 * (C - C2) = -C * C2
Divide both sides by (C - C2) to solve for C1:
C1 = (-C * C2) / (C - C2)
Now, let's compare this solution to the answer choices provided:
a.) C1 = CC2 / (C2 - C) -> This answer choice does not match the solution we derived.
b.) C1 = C - C2 / C -> This answer choice is also different from our solution.
c.) C1 = C + C2 / CC2 -> This answer choice does not match the solution.
d.) C1 = C + C2 / C2 -> This answer choice is the closest to our solution.
So, the correct choice would be:
d.) C1 = C + C2 / C2