98 lines
2.0 KiB
Markdown
98 lines
2.0 KiB
Markdown
# Inductors
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Inductors are similar to capacitors, but there are a few key differences:
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1. **They store energy in their magnetic field**
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2. **They resist to changes in current**
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3.
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![[inductor_schematic.png]]
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**Inductance:**
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$$
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\begin{flalign}
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&L = \frac{N^2 * A * \micro}{l} &\\\
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\\
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&L = Inductance \\
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&N = \text{Coil Turns} \\
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&A = \text{Area of the coild} \\
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&\micro = \text{Permeability} \\
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&\textit{How easily a magnetic field can be crated} \\
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&l = \text{Length of coil} \\
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\end{flalign}
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$$
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### Inductors in Parallel
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$\displaystyle \frac{1}{L_{t}} =\frac{1}{L_{1}}+\frac{1}{L_{2}}+...+\frac{1}{L_{n}}$
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### Inductive Reactance
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Is the strength of opposition to alternating current in an inductor, measured in $\ohm$
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$$
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\begin{flalign}
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&X_{L} = 2\pi fL&&\\\
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&f = Frequency \\
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&L = Inductance
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\end{flalign}
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$$
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**Example:**
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```circuitjs
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$ 1 0.000005 30.13683688681966 45 5 43 5e-11
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v 144 256 144 128 0 1 10000 5 0 0 0.5
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l 240 128 240 256 0 0.03 -0.004925046545906014 0
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w 144 128 240 128 0
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w 240 256 144 256 0
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o 1 64 0 4099 5 0.025 0 2 1 3
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```
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Calculate the Inductive Reactance in this circuit:
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$$
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\begin{flalign}
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&X_{L} = 2\pi fL &\\\
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&f = 10kHz = 10.000Hz\\
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&L = 30mH = 0.03H\\
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&X_{L} = 2\pi * 10.000 * 0.03 \\
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&X_{L} \approx 1885\ohm
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\end{flalign}
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$$
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**Example 2:**
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```circuitjs
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$ 1 0.000005 30.13683688681966 45 5 43 5e-11
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v 96 256 96 128 0 1 200 5 0 0 0.5
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l 240 128 240 256 0 0.4 0.00896251184146064 0
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w 240 256 96 256 0
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r 96 128 240 128 0 200
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o 1 64 0 4099 5 0.025 0 2 1 3
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```
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Calculate the [[Resources/electricity/glossary#Impedance Z|Impedance]] in this Circuit:
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$$
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\begin{flalign}
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Z = \sqrt{R^2 + X^2} \\
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X = X_{L} - {X_{C}} \\
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\\
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X_{L} = 2\pi fL \\
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X_{L} = 2\pi * 200Hz * 400mH \\
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X_{L} = 2\pi*200*0.4H\\
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X_{L} \approx 502.65\ohm\\
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\\
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Z = \sqrt{200^2+502.65^2}\\
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Z \approx 540.97 \ohm \\
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\\
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I_{RMS} = \frac{I_{max}}{\sqrt{2}} \\
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I_{RMS} = \frac{V_{rms}}{Z} \\
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V_{RMS} = \frac{5}{\sqrt{2}} \\
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V_{RMS} \approx 3.53V \\
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I_{RMS} = \frac{3.53}{540.97} \\
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I_{RMS} \approx 6.5mA\\
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I_{max} = 0.0065 * \sqrt{2} \\
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I_{max} \approx 9.12mA \\
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\end{flalign}
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$$ |