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electrical_engineering_1:dc_circuit_transients [2022/03/23 15:58]
tfischer 		electrical_engineering_1:dc_circuit_transients [2022/11/30 01:46]
mexleadmin
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-=== Goals ===+=== Learning Objectives ===
  
-After this lesson, you should: +By the end of this section, you will be able to: 
- +  - know the time constant $\tau$ and in particularly calculate it. 
-  - know the time constant $\tau$ and in particular be able to calculate it. +  - determine the time characteristic of the currents and voltages at the RC element for a given resistance and capacitance.
-  - Be able to determine the time characteristic of the currents and voltages at the RC element for a given resistance and capacitance.+
   - know the continuity conditions of electrical quantities.   - know the continuity conditions of electrical quantities.
   - know when (=according to which measure) the capacitor is considered to be fully charged / discharged, i.e. a steady state can be considered to have been reached.   - know when (=according to which measure) the capacitor is considered to be fully charged / discharged, i.e. a steady state can be considered to have been reached.
Zeile 334: Zeile 333:
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-=== Goals === +=== Learning Objectives ===
- +
-After this lesson, you should:+
  
-  - Be able to calculate the energy content in a capacitor. +By the end of this section, you will be able to: 
-  - Be able to calculate the change in energy of a capacitor resulting from a change in voltage between the capacitor terminals. +  - calculate the energy content in a capacitor. 
-  - Be able to calculate (initial) current, (final) voltage and charge when balancing the charge of several capacitors (also via resistors).+  - calculate the change in energy of a capacitor resulting from a change in voltage between the capacitor terminals. 
 +  - calculate (initial) current, (final) voltage and charge when balancing the charge of several capacitors (also via resistors).
  
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Zeile 442: Zeile 440:
 \end{align*} \end{align*}
  
-This means that only half of the energy emitted by the source is stored in the capacitor! Again, this doesn't really sound comprehensible at first. Again, it helps to look at small packets of charge that have to be transferred from the ideal source to the capacitor. <imgref imageNo06 > shows current and voltage waveforms across the capacitor and the stored energy for different resistance values. There, too, it can be seen that the maximum stored energy (dashed line in the figure at right) is given by $\Delta W= {{1}\over{2}}$ alone. $U_s^2 \cdot C = {{1}\over{2}} \cdot (5V)^2 \cdot 1 \mu F = 12.5 \mu Ws$ is given.+This means that only half of the energy emitted by the source is stored in the capacitor! This doesn't really sound comprehensible at first. Again, it helps to look at small packets of charge that have to be transferred from the ideal source to the capacitor. <imgref imageNo06 > shows current and voltage waveforms across the capacitor and the stored energy for different resistance values. There, too, it can be seen that the maximum stored energy (dashed line in the figure at right) is given by $\Delta W= {{1}\over{2}}$ alone. $U_s^2 \cdot C = {{1}\over{2}} \cdot (5V)^2 \cdot 1 \mu F = 12.5 \mu Ws$ is given.
  
 <WRAP>  <WRAP>