Perhatikan rangkaian di bawah ini:
Tentukan:
(A) Faktor daya
(B) Daya rangkaian
\(V = 260 \sqrt{2} \sin 50t\)
\(V_{\text{max}} = 260 \sqrt{2} \text{ V}\)
\(V_{\text{eff}} = \dfrac {V_{\text{max}}}{\sqrt{2}} = \dfrac {260 \sqrt{2}}{\sqrt{2}} = 260 \text{ V}\)
\(\omega = 50 \text{ rad/s}\)
(A) Faktor daya
Reaktansi induktif
\begin{equation*} \begin{split} X_L & = \omega \:.\: L \\\\ X_L & = 50 \:.\: 300 \:.\: 10^{-3} \\\\ X_L & = 15 \: \Omega \end{split} \end{equation*}
Reaktansi kapasitif
\begin{equation*} \begin{split} X_C & = \frac {1}{\omega \:.\: C} \\\\ X_C & = \frac {1}{50 \:.\: 1000 \:.\: 10^{-6}} \\\\ X_C & = 20 \: \Omega \end{split} \end{equation*}
Impedansi
\begin{equation*}
\begin{split}
Z & = \sqrt{R^2 + (X_L - X_C)^2} \\\\
Z & = \sqrt{12^2 + (15 - 20)^2} \\\\
Z & = \sqrt{144 + 25} \\\\
Z & = \sqrt{169} \\\\
Z & = 13 \: \Omega
\end{split}
\end{equation*}
Faktor Daya
\begin{equation*}
\begin{split}
\cos \theta & = \frac {R}{Z} \\\\
\cos \theta & = \frac {12}{13}
\end{split}
\end{equation*}
(B) Daya rangkaian
\begin{equation*}
\begin{split}
V & = I \:.\: Z \\\\
260 & = I \:.\: 13 \\\\
I & = 20 \text{ A}
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
P & = V \:.\: I \:.\: \cos \theta \\\\
P & = 260 \:.\: 20 \:.\: \frac {12}{13} \\\\
P & = 4800 \text{ W}
\end{split}
\end{equation*}