35 lines
695 B
Markdown
35 lines
695 B
Markdown
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![[rlc-series-example.png]]
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Lets find out the total impedance and current of this circuit:
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$$
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\begin{flalign}
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&I = \frac{V}{Z}&\\\
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&Z = R^2 + (X_C-X_C)^2&\\
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&X_C = \frac{1}{\omega C} &\\
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&X_L = \omega C &\\
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\end{flalign}
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$$
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Lets put in some numbers
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$$
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\begin{flalign}
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&X_C = \frac{1}{2\pi*50*0.0001} \approx 31.830\ohm &\\\
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&X_L = 2\pi*50*0.15 \approx 47.123\ohm&\\
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&Z = \sqrt{12^2+(31.830-47.123)^2} \approx 19.4\ohm\\
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&I = \frac{100}{19.439} \approx 5.14A
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\end{flalign}
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$$
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Now lets finally calculate the voltage drops across all the components
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$$
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\begin{flalign}
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V_R = 5.14*12 &\approx 61.68V&\\\
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V_L = 5.14*47.13 &\approx 242.24V\\
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V_C = 5.14*31.83 & \approx 163.6V\\
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\end{flalign}
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$$
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