The resonant frequency of an oscillation in electrical circuits is given by the formula f = 1/2pÖLC. If the error in measuring L is 4%, and that measuring C is 2%, calculate the maximum percentage error in calculating f?
Many thanks
The resonant frequency of an oscillation in electrical circuits is given by the formula f = 1/2pÖLC. If the error in measuring L is 4%, and that measuring C is 2%, calculate the maximum percentage error in calculating f?
Many thanks
Hello, Stazzer5!
I think I've solved it.
Someone please check my reasoning and my work.
We are given: . . [1]The resonant frequency of an oscillation in electrical circuits
. . is given by the formula: .
If the error in measuring is 4%, and that measuring is 2%,
. . calculate the maximum percentage error in calculating ?
We have: .
Take differentials: .
Divide by
. . Hence: .
Substitute [1]: .
Therefore, the maximum percentage error in calculating is
Hello everyone
I don't know enough about electrical circuits to say for sure, but, according to this Wikipedia article, it looks as though the formula should be:It's easiest to deal with percentage errors with this type of equation if you take logs before differentiating:
So, writing as:we get:
Then on differentiating we get:
You can then substitute in the values for and as Soroban has done. (You get the same answer, 3%, but with a negative sign, indicating that if and are larger than the true value, will be smaller.)
Note that any formula where you have powers of a number of variables can be dealt with in this way:Grandad