At an AC consumer, the following functions for voltage and current were measured:
a) Determine the amplitude values $\hat{U}$, $\hat{I}$ and the RMS values $U$, $I$
RMS values:
b) Determine the frequency $f$ and the phase angle $\varphi$ in degrees (°). (Independent)
For the phase $\varphi$, we have to subtract $\varphi_i $ from $\varphi_u$.
But to get these values, both the $u(t)$ and $i(t)$ need to have the same sinusoidal function!
Therefore:
By this we get for $\varphi$ \begin{align*} \varphi &= \varphi_u - \varphi_i \\ &= 4 + {{\pi}\over{2}} - 5 \\ &= 2.14159... \\ \end{align*}
Converted in degree: \begin{align*} \varphi &= 2.14159... \cdot {{360°}\over{2\pi}} \\ &= 32.7042...° \\ \end{align*}
c) Is the measured element resistive-capacitive or resistive-inductive?
The quantities are available in the consumer arrow system. (hard)