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electrical_engineering_and_electronics_2:block12 [2026/06/10 03:04] – mexleadminelectrical_engineering_and_electronics_2:block12 [2026/06/10 03:06] (current) – mexleadmin
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 \[ \[
 \begin{align*} \begin{align*}
-U+U_{\rm I}
 = =
 U_R+U_{\rm D}. U_R+U_{\rm D}.
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 I_{\rm D} I_{\rm D}
 \approx \approx
-\frac{U_{\rm E}-U_{\rm TO}}{R}.+\frac{U_{\rm I}-U_{\rm TO}}{R}.
 \end{align*} \end{align*}
 \] \]
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 The required forward voltage depends on the semiconductor material and therefore on the color. The required forward voltage depends on the semiconductor material and therefore on the color.
  
-For a supply voltage \(U_{\rm E}\), an LED forward voltage \(U_{\rm F}\), and a desired LED current \(I_{\rm F}\), the series resistor is+For a supply voltage \(U_{\rm I}\), an LED forward voltage \(U_{\rm F}\), and a desired LED current \(I_{\rm F}\), the series resistor is
  
 \[ \[
 \begin{align*} \begin{align*}
 \boxed{ \boxed{
-R_{\rm V} = \frac{U_{\rm E}-U_{\rm F}}{I_{\rm F}}+R_{\rm V} = \frac{U_{\rm I}-U_{\rm F}}{I_{\rm F}}
 } }
 \end{align*} \end{align*}
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 \[ \[
 \begin{align*} \begin{align*}
-P_R = (U_{\rm E}-U_{\rm F})I_{\rm F} = R_{\rm V}I_{\rm F}^2 \quad \overset{!}{<} \quad P_{R, \rm max}+P_R = (U_{\rm I}-U_{\rm F})I_{\rm F} = R_{\rm V}I_{\rm F}^2 \quad \overset{!}{<} \quad P_{R, \rm max}
 \end{align*} \end{align*}
 \] \]
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 \[ \[
 \begin{align*} \begin{align*}
-{\color{blue }{I_{\rm V}}} &= \frac{U_{\rm E}-U_{\rm Z}}{R_{\rm V}} &&\text{current supplied through the series resistor},+{\color{blue }{I_{\rm V}}} &= \frac{U_{\rm I}-U_{\rm Z}}{R_{\rm V}} &&\text{current supplied through the series resistor},
 \\ \\
 {\color{green}{I_{\rm L}}} &= \frac{U_{\rm Z}}{R_{\rm L}}           &&\text{useful load current}, {\color{green}{I_{\rm L}}} &= \frac{U_{\rm Z}}{R_{\rm L}}           &&\text{useful load current},
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}=24~{\rm V}.+U_{\rm I}=24~{\rm V}.
 \end{align*} \end{align*}
 \] \]
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 R_{\rm V} R_{\rm V}
 &= &=
-\frac{U_{\rm E}-U_{\rm F}}{I_{\rm F}}+\frac{U_{\rm I}-U_{\rm F}}{I_{\rm F}}
 \\ \\
 &= &=
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 P_R P_R
 &= &=
-(U_{\rm E}-U_{\rm F})I_{\rm F}+(U_{\rm I}-U_{\rm F})I_{\rm F}
 \\ \\
 &= &=
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}=12~{\rm V}.+U_{\rm I}=12~{\rm V}.
 \end{align*} \end{align*}
 \] \]
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 I_{\rm V} I_{\rm V}
 &= &=
-\frac{U_{\rm E}-U_{\rm Z}}{R_{\rm V}}+\frac{U_{\rm I}-U_{\rm Z}}{R_{\rm V}}
 \\ \\
 &= &=