Unterschiede
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ee2:task_okznhljjycuqkbsh_with_calculation [2024/07/04 00:19] (aktuell) mexleadmin angelegt |
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+ | {{tag> | ||
+ | |||
+ | # | ||
+ | <fs medium> | ||
+ | A coil has an inductive reactance of $X_0 = X(f_0) = 80~\rm \Omega$ at a frequency $f_0 = 60 ~\rm kHz$. \\ | ||
+ | Calculate the frequencies $f_1$, $f_2$, $f_3$ at which the following reactances are measured: \\ | ||
+ | * $X_1 = 50 ~\rm \Omega$ | ||
+ | * $X_2 = 121 ~\rm \Omega$ | ||
+ | * $X_3 = 147 ~\rm \Omega$ | ||
+ | |||
+ | # | ||
+ | |||
+ | There are multiple ways to solve this question. \\ One way would be, to calculate the inductance $L$ first by rearranging $X(f) = 2\pi \cdot f \cdot L$. \\ \\ | ||
+ | Another way uses ratios (or "rule of three" | ||
+ | Therefore one can set up two formulas $X_n = f_n \cdot k$, $X_0 = f_0 \cdot k$, and divide the formulae by each other. \\ | ||
+ | This leads to: | ||
+ | \begin{align*} | ||
+ | {{X_n}\over{X_0}} &= {{f_n}\over{f_0}} \\ | ||
+ | f_n & | ||
+ | = {{f_0}\over{X_0}}\cdot X_n \\ | ||
+ | \end{align*} | ||
+ | |||
+ | Putting in the numbers: | ||
+ | \begin{align*} | ||
+ | f_n &= {{60 ~\rm kHz}\over{80~\rm \Omega}}\cdot X_n \\ | ||
+ | & | ||
+ | \end{align*} | ||
+ | |||
+ | # | ||
+ | |||
+ | # | ||
+ | * $f_1 = 37.5~\rm kHz$ | ||
+ | * $f_2 = 90.75~\rm kHz$ | ||
+ | * $f_3 = 110.25~\rm kHz$ | ||
+ | # | ||
+ | |||
+ | |||
+ | # |